SOLUTION: The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., after what tim

Question 1024528: The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., after what time will they change again simultaneously?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We want the Least Common Multiple (LCM) of 42, 72, 108
:
Consider the prime factors of each number
:
42 = 2 * 3 * 7
:
72 = 2^3 * 3^2
:
108 = 2^2 * 3^3
:
we select each unique prime factor
:
2^3 * 3^3 * 7 = 1512 seconds
:
note that 2^3 includes the prime factors 2 and 2^2
note that 3^3 includes the prime factors 3 and 3^2
:
now divide 1512 by 60 = 25.2 minutes
:
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After 25 minutes and 12 seconds, all three lights will change simultaneously
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