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Robert has built a mechanical model solar system with three balls representing planets at the end of rods attached to the centre representing the sun. The planets are aligned when he turns on the motor. The innermost planet makes a revolution in 12 seconds, the middle planet makes a revolution in 30 seconds, and the outermost planet makes a revolution in 42 seconds. After how many seconds will the planets be aligned again?

Verified Answer :

VenusRetrograde

Answer=420seconds

To solve this problem, we must solve for the least common multiple of these three numbers. We do this by first finding the prime factorization of each number.

Prime factorization of 12 = 2 2 3 = 2²  3\(^{1}\)  5\(^{0}\)
Prime factorization of 30 = 2 3 5 = 2\(^{1}\)  3\(^{1}\)  5\(^{1}\)
Prime factorization of 42=237=2\(^{1}\)3\(^{1}\)7\(^{1}\)

Using the set of prime numbers with the highest exponent value we get:

LCM=\(2^{2} *3 ^{1} *5 ^{1} *7 ^{1} =4*3*5*7=420\)

It will take 420seconds for the planets to be aligned again.


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