# math

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A bell rings every 2 hours, a second bell rings every 3 hours, and a third bell rings every 4 hours. If all 3 bells ring at 9:00 AM. , at what time will all 3 bells next ring?

• math -

If you have not learned about LCM before, then you can make a list:
9:00 11 13 15 17 19 21 23:00
9:00 12 15 18 21 0:00
9:00 13 17 21 01:00
21:00 = 9:00 pm is the next time all three bells will ring together.

If you are familiar with LCM, then the intervals are 2,3 and 4 hours.
The LCM of 2, 3 is 6 hours,
the LCM of 3,4 is 12,
the LCM of 2,4 is 4.

So take the longest period of 12 hours and add to 9:00am to get 9:00pm.

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