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

To find the next time they will change simultaneously, we have to find the LCM of $48, 72$ and $108$ seconds.
$\begin{matrix} 2 & 48, 72, 108 2 & 24, 36, 54 2 & 12, 18, 27 2 & 6, 9, 27 3 & 3, 9, 27 3 & 1, 3, 9 3 & 1, 1, 3 1, 1, 1 \end{matrix}$
$∴$ LCM is $2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 432$ seconds
Therefore they will after $432$ seconds or $420 + 12 = 6$ minutes $12$ seconds.
Thus, they will meet again at $8 a m + 6$ minutes $12$ seconds $= 8 : 06 : 12 a m$
or
approx. at $8 : 06 a m$ .

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

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 ?