The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change together at 8:20 a.m., at what time will they next change together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8:27:12 a.m.
Each light changes at multiples of its own interval, so all three change together again after the smallest time that is a multiple of all three intervals, their LCM.
\(48=2^{4}\times3\), \(72=2^{3}\times3^{2}\), \(108=2^{2}\times3^{3}\)
LCM \(=2^{4}\times3^{3}=432\) seconds
\(432\) seconds \(=7\) minutes 12 seconds, since \(7\times60=420\)
8:20:00 a.m. \(+\) 7 min 12 s \(=\) 8:27:12 a.m.
They next change together at 8:27:12 a.m.