Six bells ring at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. Once, when they start ringing simultaneously for the first time, then determine how many times they will ring together in a continuous span of 30 minutes?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16 times
Bells that start together ring together again after a time that is a multiple of every interval; the first such time is the LCM of the intervals.
LCM of 2, 4, 6, 8, 10 and 12 \(=120\) s \(=2\) minutes
In 30 minutes they ring together again \(30\div2=15\) times
Counting the first ring at the start: \(15+1=16\) times
Tip: Dividing the period by the LCM counts only the rings after the start. The question counts the first ring as well, so add 1; 15 times (Option 2) leaves it out.