Answer:
They will next toll together at 2 o'clock A.M.
Step-by-step explanation:
Given
Three Bells toll at regular interval of 15 minutes 16 minutes and 36 minutes respectively
They will ring together after time which will be LCM of 15, 16 and 36 minutes.
lets find LCM of 15,16,36
15 = 3*5
16 = 2*2*2*2 = 2^4
36 = 2*2*3*3 = 2^2 * 3^2
LCM is found by taking the highest power of each prime factor
highest powered value of prime factors 2,3 and 5 is
5 is 5
2 is 2^4
3 is 3^2
thus, LCM = 2^4*3^2*5 = 16*9*5 = 720
Thus, they will ring together after 720 minutes
now
60 minutes = 1 hour
1 minutes = 1/60 hour
720 minutes = 720/60 hour = 12 hour.
Given that they rang together at 2 o'clock p.M
they will ring together after 12 hours at 2 PM
2 PM + 12 hours = 2 AM
Thus,
They will next toll together at 2 o'clock A.M.
