Using prime factorisation, find the HCF and LCM of 48 and 180.

Step-by-step solution

1. Write each number as a product of prime powers. $48=2^{4}cdot3$. $180=2^{2}cdot{3}^{2}cdot5$.
2. The HCF is the product of the common prime powers with the smallest exponents: $2^{2}cdot3=12$.
3. The LCM is the product of all prime powers with the largest exponents: $2^{4}cdot{3}^{2}cdot5=720$.
4. So, HCF$=12$ and LCM$=720$.

Concept tested: HCF and LCM by prime factorisation

Published 16 October 2026 · How this solution was prepared and checked