Find the LCM of the given numbers by prime factorisation method:

(i) 27, 90

(ii) 36, 48, 210

(i) 27, 90

Prime factorisation of the given numbers are:

27 = 3 × 3 × 3

90 = 2 × 3 × 3 × 5

Maximum power of 2 is 1 (in 90), 3 is 3 (in 27), and 5 is 1 (in 90).

Hence, LCM of 27 and 90 = 2 × 3 × 3 × 3 × 5 = 270.

(ii) 36, 48, 210

Prime factorisation of the given numbers are:

36 = 2 × 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

210 = 2 × 3 × 5 × 7

Maximum power of 2 is 4 (in 48), 3 is 2 (in 36), 5 is 1 (in 210), and 7 is 1 (in 210).

Hence, LCM of 36, 48 and 210 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 5040.