SOLUTION: Three lighthouses on three nearby islands flash their lighys every evening. On one island, the light flashes every 45 seconds. The lighthouse on the second island has a light that

Question 104964: Three lighthouses on three nearby islands flash their lighys every evening. On one island, the light flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light ecery 1 1/4 minutes. Suppose all thr light flash together at 8:35 p.m.

At what time will all three lights flash together again?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Convert all of the time to seconds so you have the same units.
P1 = 45 seconds
P2 = 2 minutes = 120 seconds
P3 = 1 1/4 minutes = 75 seconds
This problem is similar to finding the least common multiple (LCM) for a fraction.
Break the numbers into their prime factors.
Find the largest powers of each prime factor.
Calculate the product of all of the largest powers of the prime factors.

The prime factors are 2,3,and 5 with the highest power highlighted.

LCM = 1800 seconds. So every 1800 seconds after 8:35 PM, the lights will all blink simultaneously.
1800 seconds = 30 minutes
8:35 PM + 30 minutes = 9:05 PM.
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