Problema Solution
The earth, Jupiter, Saturn, and Uranus all revolve around the sun. The earth takes 1 yr, Jupiter 12 yrs, Saturn 30 yrs, and Uranus 84 yrs to make a complete revolution. How often will Jupiter, Saturn, and Uranus have the same position in the night sky as seen from the Earth. (Hint: To find out, you find the LCM of 12, 30, and 84. It will be that number of years.)
Answer provided by our tutors
to find the LCM, first find the prime factorizations of each number
1 = 1
12 = 2*2*3
30 = 2*3*5
84 = 2*2*3*7
now take each number the most amount of times it appears it one list & multiply them together
LCM: 1*2*2*3*5*7 = 420
they will all have the same position after 420 years