1. Venn Diagrams to find the HCF and LCM

2. 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.

3. 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

4. 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.

5. 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).

6. 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

7. 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

8. 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

9. 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

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

11. 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

12. 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

13. 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

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

15. 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

16. End