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?
Explanation
The easiest way to do this is by looking at the third bell that only rings every 4 hours. You can immediately find a solution by multiplying Bell 3 x Bell 2 = \(4 \times 3\) = 12. Because 12 is also evenly divisible by 2, this is a solution, but you don't know if this is the best solution.
To verify it is the best alternative, you must look at each time the third bell rings and determine if it's evenly divisible by the other two. Therefore, you would look at 4, 8, and 12.
Because 12 is the only bell that is evenly divisible by Bells 1 and 2, you know the bells will all ring every 12 hours. 9:00 AM = 12 hours = 9:00 PM
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