Seven bells ring at intervals of 2, 3, 4, 6, 8, 9, and 12 minutes, respectively. They started ringing simultaneously at 7:10 a.m. What will be the next time when they all ring simultaneously?

Correct option is A

Given:

Bell intervals: 2, 3, 4, 6, 8, 9, 12 minutes.

Initial simultaneous ring time: 7:10 a.m.

Solution: ​

Prime Factorization:

2 = 2

3 = 3

4 = $$2^2$$​​

6 = $$2 \times 3$$​​

8 = $$2^3$$​​

9 = $$3^2$$​​

12 = $$2^2 \times 3$$​​

LCM = $$2^3 \times 3^2 = 8 \times 9$$​ = 72 minutes
The bells will ring together again after 72 minutes.
Since they started ringing at 7:10 a.m., we add 72 minutes to this time. 7:10 a.m. + 72 minutes = 8:22 a.m.