Four bells toll after an interval of 8, 9, 12, and 15 minutes respectively. These bells begin to toll together at 3 p.m. At what time will they next toll together?

Given,

Four bells toll after an interval of 8,9,12,15 minutes, respectively. These bells begin to toll together at 3.p.m.

To find out time when they will toll together next, we will calculate the L.C.M of given numbers.

Prime Factors of 8 = 2 × 2 × 2

Prime Factors of 9 = 3 × 3

Prime Factors of 12 = 2 × 2 × 3

Prime Factors of 15 = 3 × 5

L.C.M with highest power of prime factors = 2 × 2 × 3 × 2 × 3 × 5

L.C.M = 360

That mans that the four balls toll together after 360 minutes.

Now, 60 minutes = 1 hour

= 6 hours

Since, it is given that the bells begin to toll together at 3 p.m

So, the next toll of the four bells together will be after 6 hours.

Thus 3 p.m + 6 hours

⇒ 9 p.m