Four bells ring at intervals of 9, 12, 15 and 18 seconds respectively. They start ringing together at 10:00 a.m. At what time will they next ring together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10:03 a.m.
Each bell rings at multiples of its own interval, so all four ring together again after the smallest time that is a multiple of every interval, the LCM.
\(9=3^{2}\), \(12=2^{2}\times3\), \(15=3\times5\), \(18=2\times3^{2}\)
LCM \(=2^{2}\times3^{2}\times5=180\) seconds
\(180\div60=3\) minutes
10:00 a.m. \(+\) 3 minutes \(=\) 10:03 a.m.
The bells next ring together at 10:03 a.m.
Why the other options are incorrect
Option (1) 10:02 a.m. — Incorrect. 2 minutes \(=120\) seconds, which is not a multiple of 9 or 18.
Option (3) 10:06 a.m. — Incorrect. 6 minutes is a common multiple, but not the least one; they meet earlier, after 3 minutes.
Option (4) 10:05 a.m. — Incorrect. 5 minutes \(=300\) seconds, which is not a multiple of 9 or 18.