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4a3paM7pMm0BDHC1HbEAo07qi+7hp/7jqX7dC/7lp73nlt7nz8xpgf7aSl3egKHrG6EAve7rOy7n 7e3oQL7Yvn3iYJ7ifL7iZP7nZr7pBqyMCkABpAwSkQEA1l7q2G7gqM7bqq60rJ7PZjyysT7us17u tX7uoCvtGfET7w7vjJ7t827dQo7d3n7sr75q++7n/e4DzT7eg1gUiuwRBuDuBf/rPa7lj87tQ97w Rj7RsK7s5kzx5v7B4TaLZf0RFdABJWXX8dd+8PIu7PRO7F6u3d+O2uH+3bKe6f4u6LYebgRA1hnP ERKAYTRf88CO8Div8HdO8pRu8hCP8hZd8WKNARyA9OvOER6AYTPf8aYO9bst9ZFO9a5u9YIW8cvu cVpP4eWd9BoREAA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Definition (LCM):
The least common multiple (LCM) of= two or more numb= ers is the smallest number that is the multiple of all of= the given numbers. 
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LCM and= LCD
Definition (LCM):
The least common multiple (LCM) of= two or more numb= ers is the smallest number that is the multiple of all of= the given numbers. 
Example: Find the LCM of 4 and 6.
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LCM and= LCD
Definition (LCM):
The least common multiple (LCM) of= two or more numb= ers is the smallest number that is the multiple of all of= the given numbers. 
Example: Find the LCM of 4 and 6.
The multiples of 4 are 4, 8, 12, 16, 20, 24, … 
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LCM and= LCD
Definition (LCM):
The least common multiple (LCM) of= two or more numb= ers is the smallest number that is the multiple of all of= the given numbers. 
Example: Find the LCM of 4 and 6.
The multiples of 4 are 4, 8, 12, 16, 20, 24, … 
The multiples of 6 are 6, 12, 18, 24, 30,… 
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LCM and= LCD
Definition (LCM):
The least common multiple (LCM) of= two or more numb= ers is the smallest number that is the multiple of all of= the given numbers. 
Example: Find the LCM of 4 and 6.
The multiples of 4 are 4, 8, 12, 16, 20, 24, … 
The multiples of 6 are 6, 12, 18, 24, 30,… 
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LCM and= LCD
Definition (LCM):
The least common multiple (LCM) of= two or more numb= ers is the smallest number that is the multiple of all of= the given numbers. 
Example: Find the LCM of 4 and 6.
The multiples of 4 are 4, 8, 12, 16, 20, 24, … 
The multiples of 6 are 6, 12, 18, 24, 30,… 
The smallest of their common multiples is = 12,
hence LCM {4, 6 } =3D 12.
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LCM and= LCD
I<= span lang=3DEN-US style=3D'font-size:178%;mso-fareast-language:ZH-CN'>.  Finding LCM by Searching
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LCM and= LCD
I.  Finding LCM by Searching
Given two or more numb= ers, we start with the largest= one and = list it’s multiple until we find the one that is the multip= le of all the other numbers as well.
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LCM and= LCD
I.  Finding LCM by Searching
Given two or more numb= ers, we start with the largest= one and = list it’s multiple until we find the one that is the multip= le of all the other numbers as well.
Example: Find the LCM of  8, 9, and 12.
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LCM and= LCD
I.  Finding LCM by Searching
Given two or more numb= ers, we start with the largest= one and = list it’s multiple until we find the one that is the multip= le of all the other numbers as well.
Example: Find the LCM of  8, 9, and 12.
The largest number is 12
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LCM and= LCD
I.  Finding LCM by Searching
Given two or more numb= ers, we start with the largest= one and = list it’s multiple until we find the one that is the multip= le of all the other numbers as well.
Example: Find the LCM of  8, 9, and 12.
The largest number is 12 and the multiples
of 12 are 12, 24, 36, 48, 60, 72, 84 … 
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LCM and= LCD
I.  Finding LCM by Searching
Given two or more numb= ers, we start with the largest= one and = list it’s multiple until we find the one that is the multip= le of all the other numbers as well.
Example: Find the LCM of  8, 9, and 12.
The largest number is 12 and the multiples
of 12 are 12, 24, 36, 48, 60, 72, 84 … 
The number that is also a multiple of 8 and 9
is 72.  Hence LCM{8, 9= , 12} =3D 72.
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LCM and= LCD
II. Constr= ucting the LCM
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LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
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LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0020.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5 = ;
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5 = ;
18 =3D 2 * 3 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0022.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5
18 =3D 2 * 32 
From the right hand side, take the highest deg= ree of
each prime factor which are
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5
18 =3D 2 * 32 
From the right hand side, take the highest deg= ree of
each prime factor which are 23,
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5
18 =3D 2 * 32 
From the right hand side, take the highest deg= ree of
each prime factor which are 23, 32,
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5
18 =3D 2 * 32 
From the right hand side, take the highest deg= ree of
each prime factor which are 23, 32, 5,
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5 = ;
18 =3D 2 * 3 
From the right hand side, take the highest deg= ree of
each prime factor which are 23, 32, 5, hence the
LCM of {8, 15, 18} =3D 2*32*5 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
II. Constr= ucting the LCM
a. Factor= each number completely
b. For each prime factor, take the highest = power app= eared in the factorizations then LCM is their product.<= /span>
Example: Construct the LCM of {8, 15, 18}. =
  8 =3D 23
15 =3D      3 * 5 = ;
18 =3D 2 * 3 
From the right hand side, take the highest deg= ree of
each prime factor which are 23, 32, 5, hence the
LCM of {8, 15, 18} =3D 2*32*5 =3D 8*9*5 =3D 360. 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
=  
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p;
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p; The multiples of 12 are 12, 24, 36 …
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p; The multiples of 12 are 12, 24, 36 …since 24 is also the multiple of 6 and = 8,  so the LCD is 24. 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p; The multiples of 12 are 12, 24, 36 …since 24 is also the multiple of 6 and 8,  so the LCD is 24.  So we cut it = into 24 slices and
 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p; The multiples of 12 are 12, 24, 36 …since 24 is also the multiple of 6 and 8,  so the LCD is 24.  So we cut it = into 24 slices and
 
1
8
Joe gets 24*     =3D 3 slices, =
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0034_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAX AAEAgAAAAP///wIEjI+pVgA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p; The multiples of 12 are 12, 24, 36 …since 24 is also the multiple of 6 and 8,  so the LCD is 24.  So we cut it = into 24 slices and
 
1
8
Joe gets 24*     =3D 3 slices, =
1
6
Mary gets 24*     =3D 4 slices, =
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0035_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAX AAEAgAAAAP///wIEjI+pVgA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0035_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
The LCM of the denominato= rs of a list of
fractions is called the L= CD, the least common
denominator.
Example:  We have a pizza.  Joe wants 1/8 = of it, Mary wants 1/6= of it and Chuck wants 5/12 of it.  How many equal sli= ces should we cut the pizza and how many slices should each person take?
We need LCD of 1/8, 1/6, 5/12.&nbs= p; The multiples of 12 are 12, 24, 36 …since 24 is also the multiple of 6 and 8,  so the LCD is 24.  So we cut it = into 24 slices and
 
1
8
Joe gets 24*     =3D 3 slices, =
1
6
Mary gets 24*     =3D 4 slices, =
5
12
Chuck gets 24*     =3D 10 slices.<= /span> =
2=
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0036_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAX AAEAgAAAAP///wIEjI+pVgA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0036_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0036_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAY AAEAgAAAAP///wIEjI+pVwA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0036_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAA6 ABMAgAAAAP8AAAI8hI+pF70Po1ytzotldbl7sAXfeIXkCZnoiqgs675oLK9cDd/4Se9d78MAg5Mh MWI8PpJKBbPZ2kA9ulMBADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0037.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Converting the Denominators
       
 
 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Converting the Denominators
For any fraction      ,      =3D         where c =3D 0. = ;
a
b
a
b
a*c
b*c 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0045_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0045_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAu AAEAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0045_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAP ABcAgAAAAP///wIlhI8XkQ3rGoyKUXVrfjbP+4Ebt4WU6aDpqCat253xyc6pHeFNAQA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0045_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAP///wIEjI+pVgA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Converting the Denominators
For any fraction      ,      =3D         where c =3D 0. = ;
a
b
a
b
a*c
b*c 
Example:
Convert the fraction      to denomi= nator 48.
 =
9
16
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0046_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0046_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAu AAEAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0046_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAP ABcAgAAAAP///wIlhI8XkQ3rGoyKUXVrfjbP+4Ebt4WU6aDpqCat253xyc6pHeFNAQA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0046_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0046_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAP///wIEjI+pVgA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Converting the Denominators
For any fraction      ,      =3D         where c =3D 0. = ;
a
b
a
b
a*c
b*c 
Example:
Convert the fraction      to denomi= nator 48.
Since 48 =3D 16 * = 3,
 
9
16
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0047_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0047_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAu AAEAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0047_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAP ABcAgAAAAP///wIlhI8XkQ3rGoyKUXVrfjbP+4Ebt4WU6aDpqCat253xyc6pHeFNAQA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0047_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0047_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAEAgAAAAP///wIEjI+pVgA7 ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0048.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Converting the Denominators
For any fraction      ,      =3D         where c =3D 0. = ;
a
b
a
b
a*c
b*c 
Example:
Convert the fraction      to denomi= nator 48.
Since 48 =3D 16 * = 3,
therefore       =3D=         = ;      
9
16
9 * 3
16 * 3
9
16
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LCM and= LCD
Converting the Denominators
For any fraction      ,      =3D         where c =3D 0. = ;
a
b
a
b
a*c
b*c 
Example:
Convert the fraction      to denomi= nator 48.
Since 48 =3D 16 * = 3,
therefore       =3D=         = ;     =3D 
9
16
9 * 3
16 * 3
27
48
9
16
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LCM and= LCD
Multip= lier Theorem:
 
 
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Multip= lier Theorem:
 
To conver= t a fraction      into a fraction with different =
denominat= or d, the new numerator is d*      . 
a
b
a
b
------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0042_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAP///wIFjI+py1wAO1== ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0042_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAX AAIAgAAAAP///wIGjI+pyx0FADs= ------=_NextPart_01C82DCB.2BE7C640 Content-Location: file:///C:/2253B8A4/3LCMandLCD_files/slide0043.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" LCM and LCD
LCM and= LCD
Multip= lier Theorem:
 
To conver= t a fraction      into a fraction with different =
denominat= or d, the new numerator is d*      . 
Example:  Convert       to a fraction with denominator 48. 
=
 
&#= 13;
a
b
a
b
9
16