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**Least Common Multiple (LCM) of**

2 or 3 numbers

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**Least Common Multiple (LCM)**

Finding the Least Common Multiple (LCM)

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Finding the Least Common Multiple (LCM) Example 1) Find the LCM of 12 and 15 Solution 1) 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 2) The prime factors of 12 = 2 x 2 x 3 The prime factors of 15 = x 5 LCM = = 60 2 x 2 x 3 x 5

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Finding the Least Common Multiple (LCM) Example 2) Find the LCM of 5, 6 and 10 Solution 1) 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, … The multiples of 10 are 10, 20, 30, 40, 50, … Answer: The LCM of 5, 6 and 10 30 Solution 2) The prime factors of 5 = The prime factors of 6 = 2 x 3 The prime factors of 10 = 2 x LCM = = 30 2 x 3 x 5

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**Greatest Common factor (GCF) of**

2 or 3 numbers

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**Greatest Common Factor (GCF)**

Finding the Greatest Common Factor (GCF)

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Finding the Greatest Common Factor (GCF) Example 1) Find the GCF of 12 and 15 Solution: The prime factors of 12 = 2 x 2 x 3 The prime factors of 15 = x 5 GCF = = 3 3

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**GCF = 1 Finding the Greatest Common Factor (GCF)**

Example 2) Find the GCF of 5, 6 and 10 Solution: The prime factors of 5 = The prime factors of 6 = 2 x 3 The prime factors of 10 = 2 x no common factor GCF = 1

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**LCM = = 120 GCF = = 4 Finding the LCM and GCF**

Example 2) Find the LCM and GCF of 8, 12 and 20 Solution: LCM: The prime factors of 8 = x 2 x 2 The prime factors of 12 = 2 x 2 x The prime factors of 20 = 2 x 2 x LCM = = 120 2 x 2 x 2 x3 x 5 Solution: GCF: The prime factors of 8 = x 2 x 2 The prime factors of 12 = 2 x 2 x The prime factors of 20 = 2 x 2 x GCF = = 4 2 x 2

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**Link to Practice Online**

Finding the LCM Finding the GCF

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