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 =(QA,\Sigma ,\delta A, q0A, FA) and B =(QB,\Sigma ,\delta B, q0B, FB), how many states will the new machine have?

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