# 6. The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

P Pankaj Sanodiya

The time period after which these lights will change = LCM of 48, 72 and 108

$\begin{array}{|c|c|}\hline 2 & {48,72,108} \\ \hline 2 & {24,36,54} \\ \hline 2 & {12,18,27} \\ \hline 2 & {6,9,27} \\ \hline 3 & {1,3,9} \\ \hline 3 & {1,1,3} \\ \hline 3 & {1,1,1} \\ \hline\end{array}$

LCM=2 $\times$$\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3 = 432

They will change together after every 432 seconds i.e., 7 min 12 seconds.

Hence, they will change simultaneously at 7:07:12 am.

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