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**Use of Venn Diagrams to find the HCF and LCM**

Number

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**Find the HCF and LCM of 24 and 60 **

Use a factor tree to help you find the Prime Factors Then a Venn Diagram to help you find the HCF and LCM Can you remember how to draw a Factor Tree?

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**Prime Factors have now been found. **

FACTOR TREES 24 60 4 6 4 15 2 2 2 3 2 2 3 5 Prime Factors have now been found

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**We now need to find the HCF**

Prime Factors 24 = 2 x 2 x 2 x 3 60 = 2 x 2 x 3 x 5 We now need to find the HCF - Highest Common Factor and the LCM - Lowest Common Multiple

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**Venn Diagram HCF is the region of intersection 24 = 2 x 2 x 2 x 3**

60 24 2 2 5 2 LCM is all the numbers in the circles multiplied together 2 x 2 x 2 x 3 x 5=120 3 HCF = 2 x 2 x 3 = 12 LCM = 2 x 2 x 2 x 3 x 5 = 120

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**or you could write out the multiples of 24 and 60**

The LCM of two or more numbers is the smallest number that is a multiple of each of the numbers. 24 x 5 = x 2 =120 or you could write out the multiples of 24 and 60 24, 48, 72, 96, 120, 144,…. 60, 120, 180, 240, 300,.... The HCF of two or more numbers is the largest number that divides exactly into each of them. 24 ÷ 12 = ÷ 12 = 5

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**Can you do some questions**

now on your own?

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**Find the HCF and LCM of the following:**

Answers: HCF = 3, LCM = 30 HCF = 10, LCM = 60 HCF = 14, LCM = 42 HCF = 6, LCM = 1080

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