  We bound the greatest common divisor of two coprime multivariable polynomials
evaluated at algebraic numbers, generalizing work of Levin, and going towards
conjectured inequalities of Silverman and Vojta. As an application, we prove
results on greatest common divisors of terms from two linear recurrence
sequences, extending the results of Levin, who considered the case where the
linear recurrences are simple, and improving recent results of Grieve and Wang.
The proofs rely on Schmidt's Subspace Theorem.
