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 cha

Question

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 together next?

Accepted Answer

Step 1: LCM of $48$, $72$ and $108$:
$48 = 2^4 	imes 3$, $72 = 2^3 	imes 3^2$, $108 = 2^2 	imes 3^3$
LCM $= 2^4 	imes 3^3 = 432$ seconds
Step 2: $432$ seconds $= \frac{432}{60} = 7$ min $12$ sec.
$\Rightarrow$ Traffic lights will change simultaneously again at $7 : 07 : 12$ a.m.

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