NCERT · Class 10 · Mathematics · Real NumbersFind the HCF and LCM of 12, 15 and 21 using the prime factorization method.

First, find the prime factorizations: 12 = 2² × 3, 15 = 3 × 5, and 21 = 3 × 7. The HCF is the product of the smallest power of each common prime factor, which is 3 because 3 appears in all three factorizations. The LCM is the product of the greatest power of all prime factors, which is 2² × 3 × 5 × 7 = 4 × 3 × 5 × 7 = 420. Thus, HCF is 3 and LCM is 420.