Use of Venn Diagrams to find the HCF and LCM

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Use of Venn Diagrams to find the HCF and LCM

• Number

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• Find the HCF and LCM of 24 and 60
• Use a factor tree to help you find the
  Prime Factors
• Then a Venn Diagram to help you find the HCF
  and LCM
• Can you remember how to draw a Factor Tree?

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FACTOR TREES
24
60
4
15
6
4
2
2
2
3
2
2
3
5
Prime Factors have now been found. ?
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Prime Factors

• 24 2 x 2 x 2 x 3
• 60 2 x 2 x 3 x 5

We now need to find the HCF
- Highest Common Factor
and the LCM
- Lowest Common Multiple
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Venn Diagram
HCF is the region of intersection 2 x 2 x 3 12
24 2 x 2 x 2 x 3 60 2 x 2 x 3 x 5
60
24
2
2
5
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LCM is all the numbers in the circles multiplied
together 2 x 2 x 2 x 3 x 5120
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HCF 2 x 2 x 3 12
LCM 2 x 2 x 2 x 3 x 5 120
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The LCM of two or more numbers is the smallest
number that is a multiple of each of the
numbers. 24 x 5 120 60 x 2 120 or you
could write out the multiples of 24 and 60 24,
48, 72, 96, 120, 144,. 60, 120, 180, 240,
300,.... The HCF of two or more numbers is the
largest number that divides exactly into each of
them. 24 12 2 60 12 5
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Can you do some questions now on your own?
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Find the HCF and LCM of the following

• 6 and 15
• 20 and 30
• 14 and 42
• 24, 30 and 54

• Answers
• HCF 3, LCM 30
• HCF 10, LCM 60
• HCF 14, LCM 42
• HCF 6, LCM 1080