# HCF, LCM, prime factor tree - St Sampsons High School Highest Common Factor Lowest Common Multiple using prime factor trees David Weeks www.Mathsmadeeasy.co.uk Permission given to use for non-commercial use Find the HCF of 60 and 72 Find the LCM of 60 and 72 Find the HCF of 48 and 56 Find the LCM of 48 and 56 Alter animation effects as appropriate play as slide show You will learn how to Make a Prime Factor Tree Find the HCF of two numbers Find the LCM of two numbers Highest Common Factor HCF Take two numbers 8

10 2 Whats the biggest number that will go into both? 2 goes into 8 four times 8 2 = 4 2 goes into 10 five times 10 2 = 5 Theres no bigger number than 2 that goes into both So its the biggest FACTOR or the Highest Common Factor Lowest Common Multiple LCM 8 Take two numbers 40 10 If you do the times table for each at what number do they cross 1

2 3 4 5 6 7 8 16 24 32 40 48 56 64 10 20 30 40 50 60 70 80 The first time they cross is at 40 So its the Lowest Common Multiple of these two numbers 8 Finding HCF and LCM using the prime factor tree Did you know? EVERY number

is made from Prime numbers Multiplied together! The first prime number is 2, then 3, then 5, then 7. Its a number that no other number goes into except itself and one Exercise Find the HCF of 60 and 72 Find the LCM of 60 and 72 Prime Factor Tree for 60 60 Write 60 at the top of the page 60 = prime number 2 x 30 30 = prime number 2 x 15 15 = prime number 3 x prime number 5 30

2 15 2 3 5 60 is all the prime numbers 2 x 2 x 3 x 5 multiplied together Prime Factor Tree for 72 72 Write 72 at the top of the page 72 = prime number 2 x 36 36 = prime number 2 x 18 18 = prime number 2 x 9 9 = prime number 3 x prime number 3 36 2

18 2 2 9 3 3 72 is the prime numbers 2 x 2 x 2 x 3 x 3 multiplied together Finding the Highest Common Factor 72 60 2 30 2

x 15 2 3 18 2 2 5 36 2 x 2 3

Look for common factors in both trees Multiply them together = 12 9 3 12 is the biggest number that goes into both 60 and 72 So it is the Highest Common Factor 3 Finding the Lowest Common Multiple 60 2 18 2 15

3 36 2 30 2 72 5 x 72 =360 5 2 x 3 x60 =360 Look for the factors remaining in either tree 2 9

3 Cross multiply with top number in opposite tree 360 is the Lowest Common Multiple of 60 and 72 3 Exercise Find the HCF of 56 and 48 Find the LCM of 56 and 48 Prime Factor Tree for 56 56 Write 56 at the top of the page 56 = prime number 2 x 28 28 = prime number 2 x 14 14 = prime number 2 x prime number 7 28 2

14 2 2 7 56 is all the prime numbers 2 x 2 x 2 x 7 multiplied together Prime Factor Tree for 48 48 Write 48 at the top of the page 48 = prime number 2 x 24 24 = prime number 2 x 12 12 = prime number 2 x 6 6 = prime number 2 x prime number 3 24 2

12 2 2 6 2 3 48 is the prime numbers 2 x 2 x 2 x 2 x 3 multiplied together Finding the Highest Common Factor 48 56 2 28 2 x

14 2 2 12 2 2 7 24 2 x 2 2 Look for common factors in both trees

Multiply them together = 8 6 2 8 is the biggest number that goes into both 56 and 48 So it is the Highest Common Factor 3 Finding the Lowest Common Multiple 56 2 12 2 14 2

24 2 28 2 48 7 x 48 =336 7 2 x 3 x56 =336 Look for the factors remaining in either tree 2 6 2

Cross multiply with top number in opposite tree 336 is the Lowest Common Multiple of 56 and 48 3 You now know how to Make a Prime Factor Tree Find the HCF of two numbers Find the LCM of two numbers