Answer:
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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<em>Comment on finding the LCM</em>
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
