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

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Solution

Given, The traffic lights at three different road crossings changes after $48, 72, 108$ Sec.
The time when they change simultaneously $= 7$ a.m.
To find the time at when they all change simultaneously again we have to find their L.C.M.
L.C.M of $48, 72, 108$
$48 = 2 \times 2 \times 2 \times 2 \times \times 3 72 = 2 \times 2 \times \times 3 \times 3 108 = 2 \times 2 \times 2 \times 3 \times 3 \times 3$
L.C.M $= 432 s e c o n d s$
$= 7 m i n u t e 12 s e c o n d$
Thus they will meet at $7 : 07 : 12 a m$

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