Question

Using prime factorisation, find the HCF and LCM of :

(i) 36, 84 (ii) 23, 31 (iii) 96, 404

(iv) 144, 198 (v) 396, 1080 (vi) 1152, 1664

In each case, verify that:

HCF$\times$ LCM = product of given numbers.

Answer 1

(i) 36, 84

Prime factorisation:

36 = 2² x 3²

84 = 2² x 3 x 7

HCF = product of smallest power of each common prime factor in the numbers = 2² x 3 = 12

LCM = product of greatest power of each prime factor involved in the numbers = 2² x 3² x 7 = 252

(ii) 23, 31

Prime factorization:

23 = 23

31 = 31

HCF = product of smallest power of each common prime factor in the numbers = 1

LCM = product of greatest power of each prime factor involved in the numbers = 23 x 31 = 713

(iii) 96, 404

Prime factorization:

96 = 2⁵ x 3

404 = 2² x 101

HCF = product of smallest power of each common prime factor in the numbers = 2² = 4

LCM = product of greatest power of each prime factor involved in the numbers = 2⁵ x 3 x 101 = 9696

(iv) 144, 198

Prime factorization:

144 = 2⁴ x 3²

198 = 2 x 3² x 11

HCF = product of smallest power of each common prime factor in the numbers = 2 x 3² = 18

LCM = product of greatest power of each prime factor involved in the numbers = 2⁴ x 3² x 11 = 1584

(v) 396, 1080

Prime factorization:

396 = 2² x 3² x 11

1080 = 2³ x 3³ x 5

HCF = product of smallest power of each common prime factor in the numbers = 2² x 3² = 36

LCM = product of greatest power of each prime factor involved in the numbers = 2³ x 3³ x 5 x 11 = 11880

(vi) 1152, 1664

Prime factorization:

1152 = 2⁷ x 3²

1664 = 2⁷ x 13

HCF = product of smallest power of each common prime factor involved in the numbers = 2⁷ = 128

LCM = product of greatest power of each prime factor involved in the numbers = 2⁷ x 3² x 13 = 14976