1.5 Greatest Common Factor And Least Common Multiple Worksheet With Answers - College Of The Sequoias Page 4
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11c.
Begin by finding the prime factorization of each number:
(
)
(
)
(
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(
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168 = 4 • 42 = 2 • 2
= 2 • 2
= 2 • 2 • 2 • 3 • 7
• 6 • 7
• 2 • 3 • 7
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(
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210 = 10 • 21 = 2 • 5
= 2 • 3 • 5 • 7
• 3 • 7
The largest set of primes common to both lists is 2 • 3 • 7 = 42 , so the
GCF of 168 and 210 is 42.
d.
Begin by finding the prime factorization of each number:
(
)
45 = 9 • 5 = 3 • 3
• 5 = 3 • 3 • 5
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)
(
)
60 = 10 • 6 = 2 • 5
= 2 • 2 • 3 • 5
• 2 • 3
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(
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180 = 10 • 18 = 2 • 5
= 2 • 5
= 2 • 2 • 3 • 3 • 5
• 3 • 6
• 3 • 3 • 2
The largest set of primes common to all three lists is 3 • 5 = 15 , so the GCF
of 45, 60, and 180 is 15.
Two numbers whose greatest common factor is 1 (that is, they have no prime factors in common)
are called relatively prime. For example, the numbers 9 and 14 are relatively prime, since the
prime factor of 9 is 3 and the prime factors of 14 are 2 and 7, thus there are no prime factors in
common to the two lists.
The second topic in this section deals with multiples of numbers. Multiplies of a number are
values obtained from multiplication of that number by numbers. For example, the first six
multiplies of 12 are:
multiplies of 12:
12, 24, 36, 48, 60, 72, …
Now we define the least common multiple (abbreviated LCM) as the smallest common multiple
of two different numbers. Given the two numbers 18 and 24, first list the multiples of each:
multiples of 18:
18, 36, 54, 72, 90, 108, 126, 144, …
multiples of 24:
24, 48, 72, 96, 120, 144, …
So 72 is the LCM of 18 and 24, since it is the smallest number common to both lists of multiples.
Also note that 144 is common to both lists, however it is not the smallest number which is
common (that is, it is not the least common multiple).
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