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

Concept / Approach

• They toll together every LCM of the given intervals.

Step-by-step calculation
LCM(2,4,6,8,10,12) = 120 seconds30 minutes = 1800 secondsNumber of meetings = (1800 ÷ 120) + 1 = 15 + 1 = 16

Why +1?
They also toll together at time t = 0 (the very start). Since 1800 is a multiple of 120, the final instant is also included.

Final Answer
16