A lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes. If they both blink at 8:10 P. M., at what time will they next blink together

9:10 P. M.

Step-by-step explanation:

The least common multiple (LCM) of 12 and 10 is 60. The lighthouses will blink together again 60 minutes later, at 9:10 P. M.

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Comment on finding the LCM

The LCM can be found several ways. One way is to factor out the greatest common factor (GCF) and write each number in terms of that:

12 = 2*6

10 = 2*5

Then the LCM is the product of the unique factors:

LCM (12, 10) = 2*6*5 = 60

This is equivalent to dividing the product of the two numbers by their GCF:

LCM (12, 10) = 12*10/GCF (12, 10) = 12*10/2 = 60

One can also write each number in terms of its prime factors, then form the product of each of those to its highest power:

12 = 2²*3

10 = 2*5

LCM (12, 10) = 2²*3*5 = 60