3. Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25

Solutions: (i) 12, 15 and 21 Writing the product of prime factors for all the three numbers, we get, 12=2×2×3 15=5×3 21=7×3 Therefore, HCF(12,15,21) = 3 LCM(12,15,21) = 2 × 2 × 3 × 5 × 7 = 420 (ii) 17, 23 and 29 Writing the product of prime factors for all the three numbers, we get, 17=17×1 23=23×1 29=29×1 Therefore, HCF(17,23,29) = 1 LCM(17,23,29) = 17 × 23 × 29 = 11339 (iii) 8, 9 and 25 Writing the product of prime factors for all the three numbers, we get, 8=2×2×2×1 9=3×3×1 25=5×5×1 Therefore, HCF(8,9,25)=1 LCM(8,9,25) = 2×2×2×3×3×5×5 = 1800