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 $10$.

Part $I$	Part $II$
$1. \text{l.c.m.}(8, 16, 24)$	$a. 36$
$2. \text{g.c.d.}(8, 16, 24)$	$b. 48$
$3. \text{l.c.m.}(6, 12, 18)$	$c. 8$
$4. \text{g.c.d.}(6, 12, 18)$	$d. 12$
	$e. 6$

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?

Similar Questions

Find the largest number which divides $245$ and $1029$ leaving remainder $5$ in each case.

Which of the following groups correctly matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1. \text{l.c.m.}(8, 16, 24)$ $a. 36$

$2. \text{g.c.d.}(8, 16, 24)$ $b. 48$

$3. \text{l.c.m.}(6, 12, 18)$ $c. 8$

$4. \text{g.c.d.}(6, 12, 18)$ $d. 12$

$e. 6$

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