Question

Six bells commencing tolling together toll at intervals of $2,3,6,8,10$ and $12$ seconds respectively. In $30$ minutes how many times do they toll together?

Answer 1

In such questions, we need to determine the $LCM$ of given intervals.

Given intervals:

$2,3,6,8,10,12$

or

$2,3,2\times 3,2\times 4,2\times 5,2\times 2\times 3$

Hence,

$LCM=2\times 3\times 4\times 5=120$

So, all the six balls toll together in every $120secor2minutes$.

Let's say they all toll together $X$ times in $30minutes$.

Using unary rule,

$X=\frac{30}{2}=15$

All the six ring tolls together $15$ times in $30minutes$.