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.

Find the HCF and LCM of 24 and 60.

Draw factor trees for 24 and 60.

Example: 24 and 60

24

2 12

2 6

2 3

60

2 30

2 15

3 5

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

Example: 24 and 6024 = 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.

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 6024 = 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).

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 6024 = 2 2 2 3 60 = 2 2 3 5

Now put this information into a Venn diagram.

22

32 5

24 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:

Example: 24 and 60

22

32 5

24 60

Multiply the prime factors that are in the

overlap together to

find the HCF: 2 2 3 =

12

Multiply the prime factors that are in the

overlap together to

find the HCF: 2 2 3 =

12

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:

Example: 24 and 60

22

32 5

24 60 Multiply all the prime factors in

the Venn diagram together to find the

LCM:2 2 2 3 5 =

120

Multiply all the prime factors in

the Venn diagram together to find the

LCM:2 2 2 3 5 =

120

HCF = 12

LCM = 120

Example: 24 and 60

22

32 5

24 60

Make sure you

understand why this is

true…

Make sure you

understand why this is

true…

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

1. 48 and 722. 60 and 1443. 75 and 2004. 648 and 7205. 36, 63 and 108

Your Turn

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

1. 48 and 72

Answers

22

32 3

48 72

2

HCF = 24LCM = 144

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

2. 60 and 144

Answers

2 2

35 3

60 144

2

HCF = 12LCM = 720

2

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

3. 75 and 200

Answers

22

3

5

75 200

5

HCF = 25LCM = 600

2

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

4. 648 and 720

Answers

22

3

3

648 720

5

HCF = 72LCM = 6480

22

33

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

5. 36, 63 and 108

Answers

23

3

36 63

7HCF = 9LCM = 756

32

108

End