Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively.
Find LCM using prime factorization:
2 = 2 (prime number)
4 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2
10 = 2 × 5
12 = 2 × 2 × 3
Therefore, LCM (2, 4, 6, 8, 10, 12) = 2 x 2 x 2 × 3 × 5 = 120
After every 120 minutes = 2 hours, bells will toll together.
So, required number of times = (30/2 + 1) = 16 times.