The traffic lights at three different road cr | vedclass

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Question

(A) To find when the traffic lights will change simultaneously again,we need to calculate the Least Common Multiple $(LCM)$ of the given intervals: $4

Vedclass · Accepted Answer

$8: 27: 12\, hours$

Vedclass · Answer

(A) To find when the traffic lights will change simultaneously again,we need to calculate the Least Common Multiple $(LCM)$ of the given intervals: $48, 72,$ and $108$ seconds.Prime factorization of $48 = 2^4 	imes 3^1$.Prime factorization of $72 = 2^3 	imes 3^2$.Prime factorization of $108 = 2^2 	imes 3^3$.$LCM = 2^4 	imes 3^3 = 16 	imes 27 = 432$ seconds.Now,convert $432$ seconds into minutes and seconds:$432 \div 60 = 7$ minutes with a remainder of $12$ seconds.Therefore,the lights will change simultaneously after $7$ minutes and $12$ seconds.Adding this to the initial time of $8: 20: 00$ hours:$8: 20: 00 + 0: 07: 12 = 8: 27: 12$ hours.

The traffic lights at three different road crossings change after every $48\, seconds,$ $72\, seconds$ and $108\, seconds,$ respectively. If they all change simultaneously at $8: 20: 00$ $hours,$ then they will again change simultaneously at

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