1.5 Greatest Common Factor And Least Common Multiple Worksheet With Answers - College Of The Sequoias Page 8
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11The use of prime numbers throughout this section is not just as a convenience for working with
larger numbers. It also serves as a bridge to algebra, where the primes will be replaced with
2
3
5
variables x and y. For example, to find the GCF of 12x
and 8x
y , we are looking for the
y
largest expression which is common to both lists. It must contain a 4, two x’s, and a y, so the
2
GCF is 4x
y . Similarly, to find the LCM, we are looking for the smallest expression which
5
3
contains both lists. It must contain 24, five x’s, and three y’s, so the LCM is 24x
y
.
Example 5
Find the GCF and LCM of each expression.
4
5
3
6
a.
7x
y
,14x
y
8
5
10
3
b.
10a
b
, 6a
b
3
2
5
c.
4x
y
,12x
y
3
4
5
2
4
3
d.
6x
y
, 8x
y
,10x
y
Solution
a.
The common factors are 7, x (three times), and y (five times), so the GCF is
3
5
. The smallest multiple must contain 14, x (four times), and y (six
7x
y
4
6
times), so the LCM is 14x
y
.
b.
The common factors are 2, a (eight times), and b (three times), so the GCF
8
3
is 2a
b
. The smallest multiple must contain 30 (the LCM of 10 and 6),
10
5
a (ten times), and b (five times), so the LCM is 30a
b
.
3
c.
The common factors are 4, x (three times), and y, so the GCF is 4x
y . The
smallest multiple must contain 12, x (five times), and y (two times), so the
5
2
LCM is 12x
y
.
d.
The common factors are 2 (the GCF of 6, 8, 10), x (three times), and y (two
3
2
times), so the GCF is 2x
y
. The smallest multiple must contain 120
(which is the LCM of 6, 8, and 10), x (five times), and y (four times), so the
5
4
LCM is 120x
y
.
Terminology
greatest common factor (GCF)
relatively prime
multiple
least common multiple (LCM)
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