Two satellites begin orbiting a planet from the same space ship

Question

Two satellites are launched from a departing space ship orbiting a planet at the same time, in a parallel orbit to one another but traveling at different speeds. The first will complete a full rotation of the planet every 15 Earth days, the second will complete a full rotation of the planet every 25 Earth days. Assuming that there is no variation in their orbital behavior, how long will it take for both satellites to return to their closest possible distance? Conversely, how long will it take for both satellites to be the furthest possible distance away from one another?

Answer 1

LCM, least common multiple

of 15 and 25 = 75 days they meet again at the same original position

15= 5x3

25=5x5

75 -5x5x3

at 75/2 =37 1/2 days, they're closest, but at the opposite side of the earth

37.5/2 = 18.75 = 18 3/4 = 18 days and 18 hours is when they are furthest apart. One 1/4 around the earth, the other 3/4 around the earth.

Closest again at 37 days and 12 hours

Furthest 18 days and 18 hours