1.5 Greatest Common Factor And Least Common Multiple Worksheet With Answers - College Of The Sequoias Page 7
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11Example 4
Find the least common multiple of each set of numbers by using primes.
a.
56, 104
b.
168, 210
c.
126, 180
d.
36, 90, 216
Solution
a.
Begin by finding the prime factorization of each number:
(
)
(
)
56 = 8 • 7 = 2 • 4
• 7 = 2 • 2 • 2
• 7 = 2 • 2 • 2 • 7
(
)
(
)
104 = 4 • 26 = 2 • 2
= 2 • 2 • 2 • 13
• 2 • 13
The smallest set of primes containing both lists is 2 • 2 • 2 • 7 • 13 = 728 , so
the LCM of 56 and 104 is 728.
b.
Begin by finding the prime factorization of each number:
(
)
(
)
(
)
(
)
168 = 4 • 42 = 2 • 2
= 2 • 2
= 2 • 2 • 2 • 3 • 7
• 6 • 7
• 2 • 3 • 7
(
)
(
)
210 = 10 • 21 = 2 • 5
= 2 • 3 • 5 • 7
• 3 • 7
The smallest set of primes containing both lists is 2 • 2 • 2 • 3 • 5 • 7 = 840 ,
so the LCM of 168 and 210 is 840.
c.
Begin by finding the prime factorization of each number:
(
)
(
)
126 = 3 • 42 = 3 • 6 • 7
= 3 • 2 • 3 • 7
= 2 • 3 • 3 • 7
(
)
(
)
(
)
(
)
180 = 10 • 18 = 2 • 5
= 2 • 5
= 2 • 2 • 3 • 3 • 5
• 3 • 6
• 3 • 2 • 3
The smallest set of primes containing both lists is 2 • 2 • 3 • 3 • 5 • 7 = 1, 260 ,
so the LCM of 126 and 180 is 1,260.
d.
Begin by finding the prime factorization of each number:
(
)
(
)
36 = 6 • 6 = 2 • 3
= 2 • 2 • 3 • 3
• 2 • 3
(
)
(
)
90 = 10 • 9 = 2 • 5
= 2 • 3 • 3 • 5
• 3 • 3
(
)
(
)
(
)
(
)
216 = 8 • 27 = 2 • 4
= 2 • 2 • 2
= 2 • 2 • 2 • 3 • 3 • 3
• 3 • 9
• 3 • 3 • 3
The smallest set of primes containing both lists is
2 • 2 • 2 • 3 • 3 • 3 • 5 = 1, 080 , so the LCM of 36, 90, and 216 is 1,080.
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