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