Chapter 9.2--Expressing Fractions in Terms of the LCM of Their Denominators
Chapter 9.2--Expressing Fractions in Terms of the LCM of Their Denominators
Part 1: Finding LCM's of polynomials
To find the LCM (Least Common Multiple) of two or more numbers, we factor them and then make sure that the LCM contains enough of each factor so that it can be divided by any one of the original numbers.
Question 10 Find the LCM of the expressions:
2 x 2
3 x

3

3
 x

1


4 x

2

2
 x 2 
2 x

1
 
2
 x

1
 2
LCM= 2

3
 x

1
 2
Question 31 Now you find the LCM of the following expressions: x 2 
3 x
−
18
  x

6
 x
−
3

3
− x
 −  x
−
3
 x

LCM=
6
  x

6

 x

6
 x
−
3

Ignore the minus in front of the factor on the second line.
Part 2 Express Fractions in Terms of the LCM of Their Denominators
As in numerical fractions in order to add and subtract fractions we need to express them in terms of a common denominator.
Question 34 : Write each fraction in terms of the LCM of the denominators.
5 ab
2
,
6 ab
LCM of the denominators= ab 2
5 ab
2
,
6 b ab
2
Question 42 : Write each fraction in terms of the LCM of the denominators. b y
 y
−
4

, b
2
4 − y
LCM= y
 y
−
4
 b y
 y
−
4

,
− b
2 y y
 y
−
4

© W Clarke 1 11/18/2004

Chapter 9.2--Expressing Fractions in Terms of the LCM of Their Denominators
Question 54 :
Factor the denominators x x
−
1
2 
2 x
−
15
, x
2 x

6 x

5
LCD=
 x

5
 x
−
3
 x

1
 x
−
1
 x  5  x − 3 
,
 x  5 x
 x  1 
 x − 1  x  1 
 x  5  x − 3  x  1 
,
 x  5 x
 x
−
3

 x − 3  x  1 
Question 46 Now you write each fraction in terms of the LCM of the denominators:
2 y
−
3
,
3 y
3 − 3 y
2
2 y
−
3
, y
3
2  y − 3 
2 y
2 y
2  y
−
3

,
3 y
2  y
−
3

Question 65
 x
−
1
 3
:
will be the LCM x
2  1
 x
−
1
 3
, x  1
 x
−
1
 2
,
1 x − 1 x
2 
1
 x
−
1
 3
,
 x

1
 x
−
1

,
 x
−
1
 3
 x
−
1
 2
 x
−
1
 3
© W Clarke 2 11/18/2004