The following is a variant of a problem that appeared on a college entrance examination. In the figure below, the radius of circle A is 2 units, the radius of circle B is 3 units. Starting from the position shown in the figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle A first reach its starting point?

Find the general formula for circles of any radius. That is, let circle A have radius r, and let circle B have radius R. Find the number of revolutions in terms of r and R that circle A will make as it rolls around circle B.

The original problem on the college examination had circle A with radius 1, and the correct answer was not among the choices! (It was a multiple choice standardized test.)