Three planets take 200, 250 and 300 days respectively for one revolution around the Sun. After how many days will they all come back to the same relative position?

They realign after 3000 days.

They return together after the LCM of 200, 250 and 300.

Factorize: 200 = 2^3 x 5^2, 250 = 2 x 5^3, 300 = 2^2 x 3 x 5^2.

Take the highest powers: 2^3, 3, 5^3.

LCM = 8 x 3 x 125 = 3000.

So after 3000 days they are in the same relative position.