​Five bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 seconds respectively. In 30 minutes, how many times do they toll together? ​

Correct option is D

Given:

Five bells toll at intervals of 2, 4, 6, 8, and 10 seconds, respectively.

Concept used:

LCM = Least Common Multiple

Solution:

​LCM of 2,4,6,8, and 10

Prime factorization:

2 = 2

4 = $$2^2$$​​

6 = $$2\times3$$​​

8 = $$2^3$$​​

10 = $$2 \times5$$ 

LCM = $$2^3 \times3 \times5$$ = 120 seconds (or 2 minutes)

The bells toll together every 120 seconds (2 minutes).

In 30 minutes, the total number of 2-minute intervals is:

​$$\frac{30}{2}$$ = 15

​Include the first instance

The bells also toll together at the start (time t =0). So, they toll together 15+1=16  times in total.

The bells toll together 16 times in 30 minutes.

Thus, correct answer is (d) 16