# Use of Venn Diagrams to find the HCF and LCM

Venn Diagrams to find the HCF and LCM Whats It All About? You are going to learn: How to find the HCF or the LCM of two or more values using a Venn Diagram. What skills should you have already? You need to be able to write a number as the product of its prime factors. Example: 24 and 60 Find the HCF and LCM of 24 and 60. Draw factor trees for 24 and 60. 24 2

60 12 2 2 6 2 30 2 3 15 3

5 24 = 2 2 2 3 60 = 2 2 3 5 Example: 24 and 60 24 = 2 2 2 3 60 = 2 2 3 5 Now put this information into a Venn diagram. A Venn diagram is a visual way of representing information. A circle is used to represent each set of information. If some information is in more than one set, the circles will overlap. Example: 24 and 60 24 = 2 2 2 3 60 = 2 2 3 5 Now put this information into a Venn diagram. The rectangle and the

symbol are used to show the universal set in other words everything possible is contained within this rectangle (as in a universe). Example: 24 and 60 24 = 2 2 2 3 60 = 2 2 3 5 Now put this information into a Venn diagram. 24 60 2 2 2

3 5 Example: 24 and 60 How can this be used to find the highest common factor? The largest value that is a factor of 24 and 60 is found here : 24 60 2 2 2 3

5 Multiply the prime factors that are in the overlap together to find the HCF: 223= 12 Example: 24 and 60 How can this be used to find the lowest common multiple? The smallest value that is a multiple of 24 and 60 is found here: 24 60

2 2 2 3 5 Multiply all the prime factors in the Venn diagram together to find the LCM: 22235= 120 Example: 24 and 60

HCF LCM = 12 = 120 24 60 2 2 2 3 5 Make sure

you understand why this is true Your Turn Draw a Venn Diagram and use it to find the HCF and LCM for: 1. 2. 3. 4. 5. 48 and 72 60 and 144 75 and 200 648 and 720

36, 63 and 108 Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 1. 48 and 72 48 72 2 2 2 2 3 3

HCF = 24 LCM = 144 Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 2. 60 and 144 60 144 2 5 2 3

2 2 3 HCF = 12 LCM = 720 Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 3. 75 and 200 75 200 3

2 5 5 2 2 HCF = 25 LCM = 600 Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 4. 648 and 720 648 720

3 3 2 2 2 3 3 2 5 HCF = 72 LCM = 6480 Answers Draw a Venn Diagram and use it to find the HCF and LCM for:

5. 36, 63 and 108 36 63 7 3 2 3 2 3 108 HCF = 9 LCM = 756

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