Question

Find the least number of $4$-digit which is divisible by $18,24$and $32.$

Answer 1

$$\begin{gathered} 18=2\times 3\times 3 \\ 24=2\times 2\times 2\times 3 \\ 32=2\times 2\times 2\times 2\times 2 \end{gathered}$$
LCM of $18,24$ and $32=2\times 2\times 2\times 2\times 2\times 3\times 3=288$
To get the smallest four-digit number that is divisible by $288,$ we have to write the multiplies of $288.$
$$\begin{gathered} 288\times 2=576 \\ 288\times 3=864 \\ 288\times 4=1152 \end{gathered}$$

Hence, the least number of $4$-digit which is divisible by $18,24$and $32$ is $1152$.