Question

Mercury, Venus and Earth complete one revolution around the sun approximately in 3 months, 7 months and 12 months respectively. If the planets begin to line up, assuming them to be in the same plane, what is the minimum time required by them to align up again?

a) 4 years
b) 5 years
c) 6 years
d) 7 years​

Answer 1

Answer: 7 YEARS

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.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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Step-by-step explanation:

Answer 2

Given:

Mercury, Venus and Earth complete one revolution around the sun approximately in 3 months, 7 months and 12 months respectively.

To find: the minimum time required by the planets to align.

Solution:

Know that, Take LCM of the time taken by the individual planets in order to find the minimum time required for the planets to align.

Find the LCM of $3,7,12$.

$\[\begin{array}{*{20}{c}}2&\vline& {3,7,12}\\2&\vline& {3,7,4}\\3&\vline& {3,7,1}\\7&\vline& {1,7,1}\\{}&\vline& {1,1,1}\end{array}\]$

LCM$(3,7,12)=2\times2\times3\times7$

                    $=84$ months

Hence, the planet will align in next 84 months.