Download Least Common Multiple Greatest Common Factor

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
•
=3x2x2x5
• LCM = 60
What is the LCM of 6, 9 and 8?
• 6
9
8
• 6=2x3
• 9=
3x3
• 8=2x
•
2x2
=2x3x3x2x2
• LCM = 72
What is the GCF of 45 and 27?
• Factors of 45:
– 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:
–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 …