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
2
60
12
2
2
6
2
30
2
3
24 = 2  2  2  3
15
3
5
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:
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
60
2
2
2
3
5
Multiply all the
prime factors in
the Venn diagram
together to find the
LCM:
2  2  2  3  5 = 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
2
3
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
2
3
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
End