1. Finding the LCM and HCF using Prime Factor Decomposition
We found that: x 5 = 20 and 25 = 32
The highest common factor is found by using the prime factors that
are common in both numbers 2
2 x 2 x 5 = x 2 x 2 x 2 x 2 = 32 2 2 2 x
= 4
So the HCF of 20 and 32 is 4
The Lowest Common Multiple is found by using HCF,
then using all the numbers that are different
2 x 2 x 5 = x 2 x 2 x 2 x 2 = 32 2 2 5 2 2 2 2 2
HCF x x x x x
= 160
So the LCM of 20 and 32 is 160

2. Prime Factor Decomposition
Now answer these by using Prime Factor Decomposition:
Find the HCF and LCM of these pairs of numbers
24 and 36
27 and 36
32 and 48
56 and 152
2 x 2 x 2 x 3 = 24
2 x 2 x 3 x 3 = 36
HCF = 2 x 2 x 3 = 12
LCM = 12 x 2 x 3 = 72
3 x 3 x = 27
2 x 2 x 3 x 3 = 36
HCF = 3 x = 9
LCM = 9 x 2 x 2 x 3 = 108
2 x 2 x 2 x 2 x 2 = 32
2 x 2 x 2 x 2 x 3 = 48
HCF = 2 x 2 x 2 x 2 = 16
LCM = 16 x 2 x = 96
2 x 2 x 2 x 7 = 56
2 x 2 x = 152
HCF = 2 x = 4
LCM = 4 x 7 x = 1092