Three Bells toll at regular interval of 15 minutes 16 minutes and 36 minutes respectively given that they toll together at at 2 o'clock p. M. At what time will they next toll together

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.

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