SOLUTION: Mercury, Venus, and Earth revolve around the sun once every 3,7, and 12 months, respectively. If the three plants are in a straight line, what is the smallest number of months that

Question 122712: Mercury, Venus, and Earth revolve around the sun once every 3,7, and 12 months, respectively. If the three plants are in a straight line, what is the smallest number of months that pass before they line up agian?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the least common multiple of 3, 7, and 12
Write the prime-factor form of each of the nuimbers:
3 = 3
7 = 7
12 = 3*2^2
The lcm must have each factor raised to the highest power present.
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lcm = 3*7*2^2 = 84 months
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Earth will make 7 revolutions, each taking 12 months.
Venus will take 12 revolutions, each taking 7 months.
Mercury will take 28 revolutions, each taking 3 months.
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Cheers,
Stan H.
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