Three electronic devices make a beep after ev | vedclass

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Question

(A) To find the next time the devices beep together,we need to calculate the Least Common Multiple $(LCM)$ of their individual beep intervals: $48$,$7

Vedclass · Accepted Answer

$10:07:12\, a.m.$

Vedclass · Answer

(A) To find the next time the devices beep together,we need to calculate the Least Common Multiple $(LCM)$ of their individual beep intervals: $48$,$72$,and $108$.Prime factorization:$48 = 2^4 	imes 3^1$$72 = 2^3 	imes 3^2$$108 = 2^2 	imes 3^3$$LCM(48, 72, 108) = 2^4 	imes 3^3 = 16 	imes 27 = 432\, seconds$.Now,convert $432\, seconds$ into minutes and seconds:$432 \div 60 = 7\, minutes$ and $12\, seconds$.Since they last beeped together at $10:00\, a.m.$,they will next beep together at $10:00\, a.m. + 7\, minutes\, 12\, seconds = 10:07:12\, a.m.$

Three electronic devices make a beep after every $48\, seconds$,$72\, seconds$,and $108\, seconds$ respectively. They beeped together at $10:00\, a.m.$ The time when they will next make a beep together at the earliest is:

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