Least Common Multiple (LCM) of 2 or 3 numbers

Finding the Least Common Multiple

(LCM)

Finding the Least Common Multiple (LCM)

Example 1) Find the LCM of 12 and 15

The multiples of 12 are 12, 24, 36, 48, 60, 72, 84……

The multiples of 15 are 15, 30, 45, 60, 75, 90 ……

Answer: The LCM of 12 and 15 is 60

Solution 1)

Solution 2)The prime factors of 12 = 2 x 2 x 3The prime factors of 15 = 3 x 5

2 x 2 x 3 x 5LCM = = 60

Finding the Least Common Multiple (LCM)

Example 2) Find the LCM of 5, 6 and 10

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, ….The multiples of 6 are 6, 12, 18, 24,30, 36, 42, …

Answer: The LCM of 5, 6 and 10 30

Solution 1)

Solution 2)The prime factors of 5 = 5 The prime factors of 6 = 2 x 3

2 x 3 x 5LCM = = 30

The multiples of 10 are 10, 20, 30, 40, 50, …

The prime factors of 10 = 2 x 5

Greatest Common factor (GCF) of 2 or 3 numbers

Finding the Greatest Common

Factor (GCF)

Finding the Greatest Common Factor (GCF)

Example 1) Find the GCF of 12 and 15Solution:

The prime factors of 12 = 2 x 2 x 3The prime factors of 15 = 3 x 5

3 GCF = = 3

Finding the Greatest Common Factor (GCF)

Example 2) Find the GCF of 5, 6 and 10 Solution:

The prime factors of 5 = 5 The prime factors of 6 = 2 x 3

no common factor

The prime factors of 10 = 2 x 5

GCF = 1

Finding the LCM and GCF

Example 2) Find the LCM and GCF of 8, 12 and 20Solution: LCM:

The prime factors of 8 = 2 x 2 x 2The prime factors of 12 = 2 x 2 x 3

2 x 2 x 2 x3 x 5The prime factors of 20 = 2 x 2 x 5

LCM = = 120Solution: GCF:

The prime factors of 8 = 2 x 2 x 2The prime factors of 12 = 2 x 2 x 3

2 x 2The prime factors of 20 = 2 x 2 x 5

GCF = = 4

Finding the LCM

Link to Practice Online

Finding the GCF