Rajesh has four packets of candies with 18, 24, 30, and 36 candies respectively. Find the smallest number that is a common multiple of the number of candies in each packet.

Step-by-step solution

1. Prime factorise 18 → $2\cdot 3^2$.
2. Prime factorise 24 → $2^3\cdot 3$.
3. Prime factorise 30 → $2\cdot 3\cdot 5$.
4. Prime factorise 36 → $2^2\cdot 3^2$.
5. Take highest powers: $2^3$, $3^2$, $5^1$.
6. Multiply $2^3\cdot 3^2\cdot 5=8\cdot 9\cdot 5=360$.
7. Thus smallest common multiple is 360.

Concept tested: LCM of multiple numbers

Published 7 October 2026 · How this solution was prepared and checked