Circular Orbits
Source: AIME I 2007 #4
March 15, 2007
LaTeXnumber theoryleast common multipleAMC
Problem Statement
Three planets revolve about a star in coplanar circular orbits with the star at the center. All planets revolve in the same direction, each at a constant speed, and the periods of their orbits are 60, 84, and 140 years. The positions of the star and all three planets are currently collinear. They will next be collinear after years. Find .