Expected Greatest Common Divisor

Several integers X0, X1, ..., XK-1 are randomly chosen from some intervals. Namely, X0 is randomly chosen between A0 and B0, inclusive, X1 is randomly chosen between A1 and B1, inclusive, and so on. We are interested in the expected value of the greatest common divisor of the Xi which is the average of GCD(X0, X1, ..., XK-1) over all possible choices of X0, X1, ..., XK-1. In order to avoid floatin