How often will five bells toll together in on | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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?

Similar Questions

$HCF$ of $4 \times 27 \times 3125$,$8 \times 9 \times 25 \times 7$ and $16 \times 81 \times 5 \times 11 \times 49$ is

The $H.C.F.$ and $L.C.M.$ of two numbers are $12$ and $924,$ respectively. Then the number of such pairs is

The $L.C.M.$ and $G.C.D.$ of two numbers are $1530$ and $51,$ respectively. Find how many such pairs are possible?

Amit,Sucheta,and Neeti start running around a circular track and complete one round in $18 \text{ seconds}$,$24 \text{ seconds}$,and $32 \text{ seconds}$,respectively. In how many seconds will the three meet again at the starting point if they all started running at the same time?

The $LCM$ of $22, 54, 108, 135$ and $198$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module