Question
Find the HCF and LCM of 45, 60 and 75.
Solution
Prime factorization: 45 = 3² × 5 60 = 2² × 3 × 5 75 = 3 × 5² HCF: product of common prime factors with the smallest powers Common primes: 3 and 5 Smallest powers: 3¹, 5¹ HCF = 3 × 5 = 15 LCM: product of all prime factors with the highest powers Primes: 2, 3, 5 Highest powers: 2², 3², 5² LCM = 2² × 3² × 5² = 4 × 9 × 25 = 900 Answer: HCF = 15; LCM = 900.
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