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Date: _______________________________
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Least Common Multiples and Greatest Common Factors (Part 1)
Least Common Multiple (LCM) is the smallest nonzero whole
number that is a multiple of two or more whole numbers.
(See Hot Topics Section 1.4 for more details.)
Examples:
♦ The least common multiple (LCM) of 3 and 8 is 24.
Here is how you find the LCM of 3 and 8.
1) List the multiples of 3 and list the multiples of 8.
2) Look for smallest number that is the same in both lists. That’s your
LCM!
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, …
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, …
♦ The least common multiple (LCM) of 3, 9, and 12 is 36.
Here is how you find the LCM of 3, 9, and 12.
1) List the multiples of 3, list the multiples of 9, and list the multiples of
12.
2) Look for smallest number that is the same in all if the lists. That’s
your LCM!
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, …
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, …
Practice: Find the Least Common Multiples (LCM) of the
following numbers. Try to use mental math, but if you get stuck,
you can use a multiplication table or calculator.
1) Find the LCM of 8 and 12.
2) Find the LCM of 5 and 13.
3) Find the LCM of 16 and 64.
4) Find the LCM of 4, 7, and 8.
Greatest Common Factor (GCF) is the greatest number that is a
factor of two or more numbers.
(See Hot Topics Section 1.4 for more details.)
Examples:
♦ The Greatest Common Factor (GCF) of 12 and 18 is 6.
Here is how you find the GCF of 12 and 18.
1) Find all the factors of 12 and all the factors of 18.
2) Look for greatest number that is the same in both sets. That’s your
GCF!
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
♦ The Greatest Common Factor (GCF) of 12 and 18 is 6.
Here is how you find the GCF of 30, 60, and 75.
1) Find all the factors of 30, all the factors of 60 and all the factors of 75.
2) Look for greatest number that is the same in all of the sets. That’s
your GCF!
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 75: 1, 3, 5, 15, 25, 75
Practice: Find the Greatest Common Factors (GCF) of the
following numbers. Try to use mental math, but if you get stuck,
you can use a multiplication table or calculator.
1) Find the GCF of 8 and 12.
2) Find the GCF of 5 and 13.
3) Find the GCF of 16 and 64.
4) Find the GCF of 20, 32, and 36.