How often will five bells toll together in on | vedclass

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Question

(C) The time interval after which the five bells will toll together is the $L.C.M.$ of $5, 6, 8, 12,$ and $20$ seconds.Prime factorization:$5 = 5^1$$6

Vedclass · Accepted Answer

$31$

Vedclass · Answer

(C) The time interval after which the five bells will toll together is the $L.C.M.$ of $5, 6, 8, 12,$ and $20$ seconds.Prime factorization:$5 = 5^1$$6 = 2^1 	imes 3^1$$8 = 2^3$$12 = 2^2 	imes 3^1$$20 = 2^2 	imes 5^1$$L.C.M. = 2^3 	imes 3^1 	imes 5^1 = 8 	imes 3 	imes 5 = 120$ seconds.Since $120$ seconds $= 2$ minutes,the bells toll together every $2$ minutes.In one hour ($3600$ seconds),the number of intervals is $3600 \div 120 = 30$.Since the bells start tolling together at the beginning ($0$ seconds),we add $1$ to the total number of intervals.Total number of times they toll together $= 30 + 1 = 31$.

How often will five bells toll together in one hour if they start together and toll at intervals of $5, 6, 8, 12, 20$ seconds,respectively?

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