Use of Venn Diagrams to find the HCF and LCM

Number

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?

FACTOR TREES

24 60

4 6 4 15

2 2 2 3 2 2 3 5Prime Factors have now been found.

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

2460

Venn Diagram24 = 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

22

3

2 5

HCF = 2 x 2 x 3 = 12LCM = 2 x 2 x 2 x 3 x 5 = 120

HCF is the region of

intersection2 x 2 x 3 = 12

LCM is all the numbers in the circles

multiplied together 2 x 2 x 2 x 3 x 5=120

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

Can you do some questions now on your own?

Find the HCF and LCM of the following:

1. 6 and 15

2. 20 and 30

3. 14 and 42

4. 24, 30 and 54Answers:

1.HCF = 3, LCM = 30

2.HCF = 10, LCM = 60

3.HCF = 14, LCM = 42

4.HCF = 6, LCM = 1080