Least Common Multiple Greatest Common Factor

Definitions Least Common Multiple (LCM) = the smallest of common multiples Greatest Common Factor (GCF) = the largest of common factors

What is the LCM of 12 and 15? 12 15 12 = 3 x 2 x 2 15 = 3 x 5

What is the LCM of 6, 9 and 8? 6 9 8 6 = 2 x 3 9 = 3 x 3 8 = 2 x 2 x 2

What is the GCF of 45 and 27? Factors of 45: Factors of 27: 1 3 5 9 15 45 Factors of 27: 1 3 9 27 Greatest common factor = 9

What is the GCF of 16 and 18? Factors of 16: Factors of 18: 1 2 4 8 16 Factors of 18: 1 2 3 6 9 18 Greatest common factor = 2

Find 2 numbers whose LCM is 360 and GCF is 3 Make a list of the factors of 360 3･120, 4･90, 5･72, 6･60, 8･45, 9･40, 10･36, 12･30, 15･24, 18･20

Then Take out any pairs where both factors are not multiples of 3. 3･120, 6･60, 12･30, 15･24.

Finally Take out any that have an LCM other than 360. 15･24

Find the nth number of a sequence Look for a pattern in the sequence- does it go by 3’s 5’s etc Keep counting until you get to the nth number

For example Find the 25th number in the sequence - 3, 6, 9, 12, 15 …