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 24 = 2  2 2  2  3 3 60 = 2 3  2  5 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 2 2 3 2 5 60

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

HCF LCM

Example: 24 and 60

= 12 = 120 24 2 2 3 2 5 60 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. 48 and 72 2. 60 and 144 3. 75 and 200 4. 648 and 720 5. 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 3 2 2 3 HCF = 24 LCM = 144

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

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

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

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

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