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Answer :
Final answer:
The next time both lighthouses will flash at the same time, after first doing so at 4:05pm, is at 4:26pm. This is determined by calculating the Least Common Multiple (LCM) of their flashing intervals.
Explanation:
The question revolves around finding when two events, which occur at different regular intervals, synchronize. In this case, it’s about figuring out the next simultaneous flashing of two lighthouses after a given time. One lighthouse flashes every three minutes and another every seven minutes. They both flash together at 4:05pm. To find the next time they will both flash together, we calculate the Least Common Multiple (LCM) of their flashing intervals.
The LCM of 3 and 7 is 21. This means every 21 minutes, both lighthouses will flash at the same time. Since they flashed together at 4:05pm, adding 21 minutes to this time will give us the next simultaneous flash, which occurs at 4:26pm.
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The two lighthouses will flash at the same time again in 21 minutes which is 4:26pm.
When will the two lighthouses flash simultaneously again?
The least common multiple refers to the smallest multiple that two or more numbers have in common.
We will get time interval at which the two lighthouses flash simultaneously by finding the least common multiple (LCM) of 3 minutes and 7 minutes.
The prime factorization of 3 is 3
The prime factorization of 7 is 7.
The LCM is found by taking the highest power of each prime factor which is:
LCM(3, 7) = 3 * 7
LCM(3, 7) = 21 minutes
Therefore, the two lighthouses will flash simultaneously again after 21 minutes.
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