Download Investigation 3: Common Multiples and Common Factors

Study Guide
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Investigation 3: Common Multiples and Common Factors
3.1 - Riding Ferris Wheel (Choosing Common Multiples or Common Factors)
Common multiples: multiples that 2 or more numbers share
Example: Common multiples of 4 and 6 are 12, 24, 36, 48, …
Least common multiple (LCM): the smallest multiple that 2 or more numbers share
Example: The LCM of 4 and 6 is 12 because it is their smallest common multiple
Common factor: factors that 2 or more numbers share
Example: Common factors of 4 and 6 are 1 and 2
Greatest common factor (GCF): the largest factor that 2 or more numbers share
Example: The GCF of 4 and 6 is 2 because it is their largest common factor
Summary:
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The least common multiple (LCM) is one of the numbers when one number is a factor of
the other.
o Example: LCM of 6 & 24 is 24 because 6 is a factor of 24.
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The least common multiple is the product of the two numbers when their only common
factor is 1.
o Example: LCM of 4 & 7 is 28 because the only common factor of 4 and 7 is 1.
Study Guide
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3.2 - Looking at Cicada Cycles (Choosing Common Multiples)
Summary:
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13 & 17 had 1 factor in common, so the LCM of 13 and 17 is 221.
The least common multiple is the product of the two numbers because their only common
factor is 1.
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12, 14, 16 have more factors in common, so their LCM (336) will take patience to find.
The least common multiple is less than the product of 12, 14, and 16 because they have
other common factors.
3.3/3.4 - Bagging Snacks/Planning a Picnic (Choosing Common Factors)
Summary:
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One (1) is always a common factor of a pair of numbers.
The greatest common factor (GCF) of two numbers is one of the numbers if the larger
number is a multiple of the smaller.
o Example: GCF of 6 & 24 is 6 because 24 is a multiple of 6.
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The greatest common factor (GCF) of two numbers is 1 when both numbers are prime.
You use the LCM when numbers or things are repeated over and over again.
You use GCF when numbers or things have to be shared.