Six bells commence tolling together at toll at an interval of 2,4,6,8,10 and 12 seconds respectively. After how many minutes will they toll together?

Given:  Six bells commence tolling together at toll at interval of 2,4,6,8,10 and 12 seconds respectively.

To do: To find when the bells will toll together.

Solution:

The bells will toll together when at time which is a multiple of every single time interval.

Thus, we need to find the LCM of 2,4,6,8,10,12.

Prime factorization for the intervals are:

$2=2$

$4 =2^2$

$$
$2}^2$

$$
$$
$$
$$
$ 6=2\times3$

$8=2^3$

$10 = 2\times5$

$12=2\times2\times3$

${2}^3$

Hence, LCM  is$2^3\times3\times5=120$

LCM = 120

Thus, in 120 seconds or 2 minutes, they will toll together again

So answer is 2 minutes

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Updated on: 10-Oct-2022

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