Question

three bells ring at intervals of 20 minutes 30 minutes and 45 min respectively after how much time will the bells ring together again

Answer 1

After 180 minute (3 hours) the will ring together

Answer 2

The bells will ring together after 180 min i.e. 3 hours.

Solution:

Three bells ring at intervals of 20 minutes 30 minutes and 45 min respectively

LCM is the least common factor that is divisible by all the numbers. The bell will again rang together after the time which is equal to LCM of the times.  So, we need to find the LCM of 20, 30 and 45.

Factors of 20 = $1\times2\times5\times2$

Factors of 30 = $1\times2\times5\times3$

Factors of 45 = $1\times3\times5\times3$

So the LCM of 20, 30 and 45 min is = 180 min

Hence, the bells will ring together after 180 min = 3 hours.