  We study the greatest common divisor problem for torus invariant blowing-up
morphisms of nonsingular toric Fano varieties. Our main result applies the
theory of Okounkov bodies together with an arithmetic form of Cartan's Second
Main theorem, which has been established by Ru and Vojta. It also builds on
Silverman's geometric concept of greatest common divisor. As a special case of
our results, we deduce a bound for the generalized greatest common divisor of
pairs of nonzero algebraic numbers.
