Question

three bells tall at intervals of 12 minutes,15 minutes and 18 min respectively . if they start together after . what time they next tall together

Answer 1

There are given three bells

The first bell talls at every 12 minutes

The second bell talls at every 15 minutes

The third bell talls at every 18 minutes.

Now,
If all these start when will they tall together

See,

The first bell will ring in the multiples of 12. Like 12,24,36,48,60 and so on.

The second one will tall at multiples of 15
And, third one will tall at mutiples of 18.

We have to find a common number from the multiples of all three and the number should be the smallest common number.
So,
It means we have to find the Least Common Multiple or the LCM

So,
Lcm of 12,15 and 18

12 = 2*2*3

15= 3*5

18 = 2*3*3

Now,
Common numbers from :-

All rows = 3
First two = none (as 3 is already taken)
Last two=none
First and last = 2

So,
Lcm = 3*2*2*3*5 = 180

So,
All three bells will tall togetger after 180 minutes or 3 hours.

Answer 2

the lcm of 12,15,18 min is 180 so they. next tall together in 3 hours