Venn Diagrams to find the HCF and LCM

What’s 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 60 2 12 2 30 2 6 2 15 2 3 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 5 2 3

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: Multiply the prime factors that are in the overlap together to find the HCF: 2  2  3 = 12 24 60 2 2 5 2 3

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

Make sure you understand why this is true… Example: 24 and 60 HCF = 12 LCM = 120 24 60 2 Make sure you understand why this is true… 2 5 2 3

Your Turn Draw a Venn Diagram and use it to find the HCF and LCM for:

Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 1. 48 and 72 48 72 HCF = 24 LCM = 144 2 2 2 3 2 3

Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 2. 60 and 144 60 144 HCF = 12 LCM = 720 2 2 2 2 5 3 3

Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 3. 75 and 200 75 200 HCF = 25 LCM = 600 2 3 5 2 5 2

Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 4. 648 and 720 648 720 HCF = 72 LCM = 6480 3 2 2 2 2 3 3 5 3

Answers Draw a Venn Diagram and use it to find the HCF and LCM for: 5. 36, 63 and 108 36 63 7 HCF = 9 LCM = 756 3 2 3 2 3 108

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