Question

Three bells toll at intervals of 9, 12, 15 minutes. If they start tolling together, after what time will they next toll together?

Answer 1

Three bells toll at intervals of 9, 12 and, 15 minutes.
The time when they will toll together again is given by the LCM of 9, 12 and 15.

$\begin{array}{l}3\overline{)9,12,15}\\ 3\overline{)3,4,5}\\ 5\overline{)1,4,5}\\ 2\overline{)1,4,1}\\ 2\overline{)1,2,1}\\ \text{1,1,1}\end{array}$

Required time = 2² × 3² × 5
= 180 minutes
=3 h
If they start tolling together, they will toll together again after 3 h.