# 9. Find the smallest 4-digit number which is divisible by 18, 24 and 32.

LCM of 18, 24 and 32

$\begin{array}{|c|c|}\hline 2 & {18,24,32} \\ \hline 2 & {9,12,16} \\ \hline 2 & {9,6,8} \\ \hline 2 & {9,3,4} \\ \hline 2 & {9,3,2} \\ \hline 3 & {9,3,1} \\ \hline 3 & {3,1,1} \\ \hline & {1,1,1} \\ \hline\end{array}$

LCM = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3

We have to find the smallest 4-digit multiple of 288.

It can be observed that 288 $\times$ 3 = 864 and 288 $\times$ 4 = 1152.

Therefore, the smallest 4-digit number which is divisible by 18, 24, and 32 is 1152.

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