A light flashes every 2 minutes, a second light flashes every 3.5 minutes, and a third light flashes every 4 minutes. If all three lights flash together at 8 p.m., what is the next time of the day they will all flash together?
Answer (2)
The three lights flash at intervals of 2 minutes, 3.5 minutes, and 4 minutes. To find the next time when all three lights will flash together, we need to find the least common multiple (LCM) of these intervals.
The prime factorization of 2 is 2.
The prime factorization of 3.5 is 3.5 = 2 * 1.75 = 2 * 7/4 = 2 * 7/2 * 1/2 = 2 * 7/2 * 2/2 = 2 * 7/2.
The prime factorization of 4 is 2 * 2.
Therefore, the LCM of 2 minutes, 3.5 minutes, and 4 minutes is 2 * 7/2 * 2 = 28 minutes. So the next time when all three lights will flash together is 28 minutes after 8 p.m., which is 8:28 p.m.
The next time when all three lights will flash together is 8:28 p.m. This is determined by calculating the least common multiple of their flash intervals, which amounts to 28 minutes after they initially flash together at 8 p.m. Thus, they will flash together again at 8:28 p.m.
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