Four bells toll at intervals of 8,12,15,and 1 | vedclass

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Question

(A) To find when the bells toll together,we need to calculate the Least Common Multiple $(LCM)$ of $8$,$12$,$15$,and $18$.Prime factorization:$8 = 2^3

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(A) To find when the bells toll together,we need to calculate the Least Common Multiple $(LCM)$ of $8$,$12$,$15$,and $18$.Prime factorization:$8 = 2^3$$12 = 2^2 	imes 3$$15 = 3 	imes 5$$18 = 2 	imes 3^2$$LCM = 2^3 	imes 3^2 	imes 5 = 8 	imes 9 	imes 5 = 360$ seconds.This means the bells toll together every $360$ seconds,which is $360 / 60 = 6$ minutes.In one hour ($60$ minutes),the number of times they toll together is $60 / 6 = 10$ times.Since we exclude the toll at the start,the total count remains $10$.

Four bells toll at intervals of $8$,$12$,$15$,and $18$ seconds respectively. All four begin to toll together. How many times will they toll together in one hour,excluding the one at the start?

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