Question

Find the smallest $4$ digit number divisible of $18,24$ and $32$.

Answer 1

Compute the required value.

Factors of $18,24$ and $32$ are

$$\begin{gathered} 18=2\times 3\times 3 \\ 24=2\times 2\times 2\times 3 \\ 32=2\times 2\times 2\times 2\times 2 \end{gathered}$$

Thus the L.C.M. of $18,24$ and $32$ is $2\times 2\times 2\times 2\times 2\times 3\times 3=288$.

To get the smallest four digit number that is divisible by $288$, we have to write the multiples of $288.$

$$\begin{gathered} 288\times 2=576 \\ 288\times 3=864 \\ 288\times 4=1152 \end{gathered}$$

Hence $1152$ is the smallest $4$ digit number divisible of $18,24$ and $32$.