<PRE><B>Question 166873</B>
A family is moving and has a number of electronic devices in the same packing crate.  One of the devices beepes every 8 minutes, another beeps every 10 minutes and a third beeps every 12 minutes.  If all the devices beeped together at 3pm, what time will it be when the all beep together again?
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Find the least common multiple of 8, 10, and 12.
8 = 2^3
10 = 2*5
12 = 2^2*3

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The lcm must have all the prime factors to their highest power present
in the prime factor form of the various factors
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lcm = (2^3)*5*3 = 8*15 = 120 minutes = 2 hours
In 120 minutes the 8 minute beeper will cycle 120/8 = 15 times
The 10 minute beeper will cycle 12 times
The 12 minute beeper will cycle 10 times
When 120 minutes have elapsed they will all beep at once.

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If they all beep at 3pm, they will all beep again at 3pm + 2 hrs = 5pm
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Cheers,
Stan H.
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