Venn Diagrams To Find The Hcf And Lcm l1d6q

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

3

2 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 3

2

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