Question

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. In 30 hours, how many times do they toll together?

Answer 1

Six bells toll together at intervals of 2, 4, 6, 8, 10 and 12 minutes, respectively.

Prime factorisation:

2 = 2

4 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

10 = 2 × 5

12 = 2 × 2 × 3

∴ LCM (2, 4, 6, 8, 10, 12) = 2³ × 3 × 5

= 120

Hence, after every 120 minutes (i.e. 2 hours), they will toll together.

∴ Required number of times = `(30/2 + 1)` = 16