There are five bells which start ringing toge | vedclass

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Question

(A) To find when the bells ring together,we need to calculate the $L.C.M.$ of the given intervals: $3, 6, 9, 12, 15$ seconds.Prime factorization:$3 =

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(A) To find when the bells ring together,we need to calculate the $L.C.M.$ of the given intervals: $3, 6, 9, 12, 15$ seconds.Prime factorization:$3 = 3^1$$6 = 2^1 	imes 3^1$$9 = 3^2$$12 = 2^2 	imes 3^1$$15 = 3^1 	imes 5^1$$L.C.M. = 2^2 	imes 3^2 	imes 5^1 = 4 	imes 9 	imes 5 = 180$ seconds.This means the bells ring together every $180$ seconds,which is equal to $3$ minutes.In $36$ minutes,the number of times they ring together is $\frac{36}{3} = 12$ times.Since they start ringing together at the $0^{th}$ minute,we add $1$ to the result.Total times = $12 + 1 = 13$ times.

There are five bells which start ringing together at intervals of $3, 6, 9, 12$ and $15$ seconds respectively. In $36$ minutes,how many times will the bells ring simultaneously?

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