Finding the LCM and HCF using Prime Factor Decomposition We found that: 22 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 = 20 2 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 = 20 2 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

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 3 = 27 2 x 2 x 3 x 3 = 36 HCF = 3 x 3 = 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 3 = 96 2 x 2 x 2 x 7 = 56 2 x 2 x 39 = 152 HCF = 2 x 2 = 4 LCM = 4 x 7 x 39 = 1092