(i) 6, 9
Prime factorisation of 6 = 2 × 3
Prime factorisation of 9 = 3 × 3
Product of common factors = 3
Product of other factors = 2 × 3 = 6
LCM (6, 9) = 3 × 6 = 18
(ii) 8, 12
8 = 2 × 4 = 2 × 2 × 2
12 = 2 × 6 = 2 × 2 × 3
Product of common factors = 2 × 2 = 4
Product of other factors = 2 × 3 = 6
LCM = Product of common factors × Product of
other factors = 4 × 6 = 24
LCM (8, 12) = 24.
(iii) 10, 15
10 = 2 × 5
15 = 3 × 5
Product of common factors = 5
Product of other factors = 2 × 3 = 6
LCM (10, 15) = Product of common factors ×
Product of other factors = 5 × 6 = 30
(iv) 14, 42
14 = 2 × 7
42 = 2 × 21 = 2 × 3 × 7
Product of common factors = 2 × 7
Product of other factor = 3
LCM (14, 42) = Product of common factors ×
Product of other factors = 2 × 7 × 3 = 42
LCM (14, 42) = 42
(v) 30, 40, 60
30 = 3 × 2 × 5
40 = 2 × 2 × 2 × 5
60 = 2 × 3 × 2 × 5
Product of highest powers of the common factors = 3 × 23 × 5 = 120
LCM (30, 40, 60) = 120
(vi) 15, 25, 75
15 = 5 × 3
25 = 5 × 5
75 = 5 × 5 × 3
Product of the highest powers of the common factors = 3 × 52 = 3 × 25 = 75
LCM (15, 25, 75) = 75