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

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05:07:12 AM

06:00:12 AM

07:07:12 AM

03:07:02 AM

answer is C.

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Detailed Solution

Given, at three distinct road intersections, the traffic light changes every 48 seconds, 72 seconds, and 108 seconds.
Here, the factors of 48, 72 and 108 are,

48 = 2^{4} \times 3

72 = 2^{3} \times 3^{2}

108 = 2^{2} \times 3^{3}

So, the lowest common multiple LCM

(48, 72, 108) = 2^{4} \times 3^{3}

LCM = 432

seconds
Convert it into minutes,
So, 432 seconds = 7 minutes and 12 seconds [1 minute = 60 second]
Add this time in 7 AM we get,
Thus, the time = 7 A.M. + 7 minutes 12 seconds
So, the light changes simultaneously at 07:07:12 AM
Correct option is 3.

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