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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.
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).
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
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
HCF = 12LCM = 120
Example: 24 and 60
22
32 5
24 60
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
2 235 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
223
3
648 720
5
HCF = 72LCM = 64802
233
Draw a Venn Diagram and use it to find the HCF and LCM for:
5. 36, 63 and 108
Answers
233
36 637
HCF = 9LCM = 756
32
108
End