Question

Three bells toll together at intervals of 9, 12, 15 minutes. If they start tolling together, after what time will they next toll together?
(a) 1 hour
(b) $1\frac{1}{2}\mathrm{hours}$
(c) $2\frac{1}{2}\mathrm{hours}$
(d) 3 hours

Answer 1

(d) 3 hours

The L.C.M. of 9, 12 and 15 will give us the minutes after which the bells will next toll together.

$\begin{array}{l}2\overline{)9,12,15}\\ 2\overline{)9,6,15}\\ 3\overline{)\text{9, 3, 15}}\\ 3\overline{)\text{3, 1, 5}}\\ 5\overline{)\text{1, 1, 5}}\\ \text{1, 1, 1}\end{array}$
L.C.M. = 2² × 3² × 5
= 180
So,the bells will toll together after 180 min.
On converting into hours:
180/60 = 3 hours