The traffic lights at three different road cr | vedclass

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Question

(B) To find when the traffic lights will change simultaneously again,we need to calculate the Least Common Multiple $(LCM)$ of the time intervals: $24

Vedclass · Accepted Answer

$10:18:36$ am

Vedclass · Answer

(B) To find when the traffic lights will change simultaneously again,we need to calculate the Least Common Multiple $(LCM)$ of the time intervals: $24$,$36$,and $54$ seconds.Prime factorization:$24 = 2^3 	imes 3^1$$36 = 2^2 	imes 3^2$$54 = 2^1 	imes 3^3$$LCM = 2^3 	imes 3^3 = 8 	imes 27 = 216$ seconds.Convert $216$ seconds into minutes:$216 \div 60 = 3$ minutes and $36$ seconds.Adding this duration to the initial time of $10:15:00$ am:$10:15:00 + 0:03:36 = 10:18:36$ am.Therefore,the traffic lights will again change simultaneously at $10:18:36$ am.

The traffic lights at three different road crossings change after $24$ seconds,$36$ seconds,and $54$ seconds,respectively. If they all change simultaneously at $10:15:00$ am,then at what time will they again change simultaneously?

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