Find the HCF and LCM of 18 and 30.

Solution

First write prime factorizations: 18 = 2 × 3² 30 = 2 × 3 × 5 HCF (Highest Common Factor): Take common prime factors with the smallest powers. Common primes: 2 and 3 HCF = 2¹ × 3¹ = 2 × 3 = 6 LCM (Least Common Multiple): Take all primes that appear, with the highest powers. Primes: 2, 3, 5 Highest powers: 2¹, 3², 5¹ LCM = 2¹ × 3² × 5¹ = 2 × 9 × 5 = 90 Check: Product of numbers = 18 × 30 = 540 HCF × LCM = 6 × 90 = 540 (same, so correct) Answer: HCF = 6, LCM = 90.