# 5. Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

P Pankaj Sanodiya

CM of 8, 10 and 12

$\begin{array}{|c|c|}\hline 2 & {8,10,12} \\ \hline 2 & {4,5,6} \\ \hline 2 & {2,5,3} \\ \hline 3 & {1,5,3} \\ \hline 5 & {1,5,1} \\ \hline\end{array}$

LCM = 2 $\times$  2 $\times$  2 $\times$  3 $\times$ 5 = 120

We have to find the greatest 3-digit multiple of 120.

It can be seen that

120 $\times$ 8 = 960 and

120 $\times$ 9 = 1080.

Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

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