The traffic lights at three different road crossings change after every $48$ seconds, $72$ seconds and $108$ seconds. If they start changing simultaneously at $8 a . m .$ , after how much time will they change again simultaneously?

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Solution

The time when the lights will change simultaneously again will be quantity which is exactly divisible by $48, 72$ and $108$ . The least time when they change simultaneously will be given by their LCM.
Now, let us find LCM of given numbers:

Required time $= 2^{4} \times 3^{3}$
$= 432$ seconds
$= 7$ min $12$ seconds
So, the lights will change simultaneously at $8 : 07 : 12 a . m .$

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