Vojta's conjecture is a deep conjecture in Diophantine geometry, implying for example the Bombieri-Lang conjecture and the abc conjecture. In this talk, I will show some cases of the conjecture for blowup varieties. As a consequence, we derive some interesting inequalities of greatest common divisors. An important ingredient will be Schmidt's subspace theorem, both directly and indirectly through the results of Corvaja and Zannier.