# 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 ?

$\begin{array}{l}\text{Given that,}\\ \text{Traffic lights are changing colour}\ 48\ s,\ 72\ \text{s}\ \&\ 108\ s.\\ \text{It means that,}\\ \text{First light blink at:}\ 48\ s,\ 2\times48\ s,\ 3\times48\ \text{s}.........\ \left[\text{multiple of 48}\right]\\ \text{Second light blink at :}72\ s,\ 2\times72\ s,\ 3\times72\ \text{s}.......\left[\text{multiple of 72}\right]\\ \text{Third light blink at :}108\ s,\ 2\times108\ s,\ 3\times108\ \text{s}...\ \left[\text{multiple of 108}\right]\\ \text{So, we take a L.C.M of }48,\ 72\ \&\ 108\\ L.C.M\ is\ 432\ \\ \text{So, Light will be again blink at}\ 7:00\ hr\ +432\ \text{s}=7:07\ hr\ 12\ \text{s} \end{array}$

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