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 4 2 22 6 3
60
4 2 15 2 3 5
Prime 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 - Highest Common Factor HCF
and the LCM - Lowest Common Multiple
Venn Diagram
24 = 2 x 2 x 2 x 3 60 = 2 x 2 x 3 x 5 HCF is the region of intersection 2 x 2 x 3 = 12 60 2
24
2
2 3
5
LCM is all the numbers in the circles multiplied together 2 x 2 x 2 x 3 x 5=120
HCF = 2 x 2 x 3 = 12 LCM = 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 54 Answers: 1.HCF = 3, LCM = 30 2.HCF = 10, LCM = 60 3.HCF = 14, LCM = 42 4.HCF = 6, LCM = 1080