Question: If I use the product construction to create a machine that recognizes L ( A ) cup L ( B ) based on DFAs

If I use the product construction to create a machine that recognizes L(A)\cup L(B) based on DFAs A =(Q_A,\Sigma ,\delta _A, q_0A, F_A) and B =(Q_B,\Sigma ,\delta _B, q_0B, F_B), how many states will the new machine have?

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