Question

Find the least number of $3$-digit which is divisible by $6,8$ and $12.$

Answer 1

$$\begin{gathered} 6=2\times 3 \\ 8=2\times 2\times 2 \\ 12=2\times 2\times 3 \end{gathered}$$
LCM of $6,8$ and $12=2\times 2\times 2\times 3=24$
To get the smallest three-digit number that is divisible by $24,$ we have to write the multiplies of $24.$
$$\begin{gathered} 24\times 2=48 \\ 24\times 3=72 \\ 24\times 4=96 \\ 24\times 5=120 \end{gathered}$$

Hence, the least number of $3$-digit which is divisible by $6,8$ and $12$ is $120.$.