Five bells begin to toll together and then toll at intervals of 6, 7, 8, 9 and 12 seconds respectively. After how many seconds will they next toll together?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 504 seconds
Each bell tolls at multiples of its own interval, so they toll together again after the smallest time that is a multiple of all five intervals, their LCM.
\(6=2\times3\), \(7=7\), \(8=2^{3}\), \(9=3^{2}\), \(12=2^{2}\times3\)
LCM \(=2^{3}\times3^{2}\times7=504\)
They next toll together after 504 seconds.