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The Earth, Jupiter, Saturn, and Uranus all revolve around the Sun. The earth takes 1 year, Jupiter takes 12 years. Saturn takes 30 years and Uranus takes 84 years to complete one revolution around the Sun. At what periodicity, all these four planets lineup with each other?

The Earth, Jupiter, Saturn, and Uranus all revolve around the Sun. The earth takes 1 year, Jupiter takes 12 years. Saturn takes 30 years and Uranus takes 84 years to complete one revolution around the Sun. At what periodicity, all these four planets lineup with each other? Correct Answer 420 years

Concept:

To find the year at the all the planet will be line up to each other we have to find the Least Common Multiple ( LCM ) of revolution time of each year.

Calculation:

Given:

Revolution time around sun of Earth = 1 years, Jupiter = 12 years, Saturn = 30 years, Uranus = 84 years

To find LCM expressed each revolution in product of prime no,

1 = 1

12 = 2 × 2 × 3

30 = 2 × 3 × 5

80 = 2 × 2 × 3 × 5

Now LCM = 1 × 2 × 2 × 3 × 5 × 7

LCM = 420

Hence Planets will lineup with each other periodically after 420 years.

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