Question

Using prime factorisation, find the HCF and LCM of

(i) 144, 198
(ii) 396, 1080
(iii) 1152, 1664

Answer 1

(i) 144, 198
Prime factorisation:
144 = $2^4\times 3^2$
198 = $2\times 3^2\times 11$
​ HCF = product of smallest power of each common prime factor in the numbers = $2\times 3^2$ = 18
LCM = product of greatest power of each prime factor involved in the numbers = $2^4\times 3^2\times 11$ = 1584

(ii) 396, 1080
Prime factorisation:
396 = $2^2\times 3^2\times 11$
1080 = $2^3\times 3^3\times 5$
​ HCF = product of smallest power of each common prime factor in the numbers = $2^2\times 3^2$ = 36
LCM = product of greatest power of each prime factor involved in the numbers = $2^3\times 3^3\times 5\times 11$ = 11880

(iii) 1152 , 1664
Prime factorisation:
1152 = $2^7\times 3^2$
1664 = $2^7\times 13$
HCF = product of smallest power of each common prime factor involved in the numbers = $2^7$ = 128
LCM = product of greatest power of each prime factor involved in the numbers = $2^7\times 3^2\times 13$ = 14976