Question

Suppose that, in some distant part of the universe, there is a star with four orbiting planets . One planet makes a trip around the star in 6 earth years , the second planet takes 9 earth years, the third takes 15 earth years and the fourth takes 18 earth years . Suppose that at some time the planets are lined up. How many years will it take for them to all line up

Answer 1

Answer: 90 Earth years.

Step-by-step explanation:

Analizing the information provided in the exercise, you need to find the Least Common Multiple (LCM) of the given numbers.

You can follow these steps:

1. You must descompose 6, 9, 15 and 18 into their prime factors:

$6=2*3\\\\9=3*3=3^2\\\\15=3*5\\\\18=2*3*3=2*3^2$

2. Finally, you need to choose the commons and non commons with their greatest exponents and multiply them. Then you get:

$L.C.M=2*3^2*5=2*9*5\\\\L.C.M=90$

Therefore, it will take 90 Earth years for them to all line up.