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

(i) 28, 98

(ii) 36, 40, 126

(iii) 108, 135, 162

(iv) 24, 28, 196

(i) 28, 98

Prime factorisation of the given numbers are:

28 = 2 × 2 × 7

98 = 2 × 7 × 7

2 occurs as a prime factor maximum 2 times and 7 also 2 times.

Hence, LCM of 28 and 98 = 2 × 2 × 7 × 7 = 196.

(ii) 36, 40, 126

Prime factorisation of the given numbers are:

36 = 2 × 2 × 3 × 3

40 = 2 × 2 × 2 × 5

126 = 2 × 3 × 3 × 7

2 occurs as a prime factor maximum 3 times, 3 occurs 2 times, 5 occurs 1 time and 7 also 1 time.

Hence, LCM of 36, 40 and 126 = 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520.

(iii) 108, 135, 162

Prime factorisation of the given numbers are:

108 = 2 × 2 × 3 × 3 × 3

135 = 3 × 3 × 3 × 5

162 = 2 × 3 × 3 × 3 × 3

3 occurs as a prime factor maximum 4 times, 2 occurs 2 times and 5 occurs 1 time.

Hence, LCM of 108, 135 and 162 = 2 × 2 × 3 × 3 × 3 × 3 × 5 = 1620.

(iv) 24, 28, 196

Prime factorisation of the given numbers are:

24 = 2 × 2 × 2 × 3

28 = 2 × 2 × 7

196 = 2 × 2 × 7 × 7

2 occurs as a prime factor maximum 3 times, 3 occurs 1 time and 7 also 2 times.

Hence, LCM of 24, 28 and 196 = 2 × 2 × 2 × 3 × 7 × 7 = 1176.