What is the least common multiple of 12, 18 and 24?

हल

1. 01

   Write each number as a product of prime factors: $12 = 2^2 \times 3$, $18 = 2 \times 3^2$ and $24 = 2^3 \times 3$.

2. 02

   The LCM takes the highest power of each prime that appears anywhere: $2^3$ from 24 and $3^2$ from 18.

3. 03

   So the LCM is $2^3 \times 3^2 = 8 \times 9 = 72$.

4. 04

   Check: $72 \div 12 = 6$, $72 \div 18 = 4$ and $72 \div 24 = 3$, all whole numbers.