No, the lights of the maritime lighthouse cannot trigger again after 360 seconds.
The green light of the lighthouse flashes every 56 seconds, which means it will flash after 56, 112, 168, 224, 280, and 336 seconds. However, none of these intervals are divisible by 180 seconds, the interval at which the main light flashes.
The intervals at which the main light flashes are 180, 360, 540, 720, etc. seconds. So, the next time the main light will flash after midnight is at 360 seconds.
Since the smallest common multiple of 56 and 180 is 5040 seconds, we need to find the next time after 360 seconds when both lights will flash together, which is the next multiple of 5040.
360 + 5040 = 5400 seconds
5400 seconds is the next time when both lights will go off at the same time. Therefore, after 360 seconds, the lights of the maritime lighthouse will not trigger again together.
The light of a maritime lighthouse flashes every 180 seconds. Its green light flashes every 56 seconds. At midnight, both lights go off at the same time. Can they trigger again after 360s? Justify
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