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We apply a quantum mechanical/molecular mechanical (QM/MM) multiscale approach to calculate the segregation energies of Mg and Pb to two kinds of grain boundaries in Al. The first boundary, a symmetric (310)[001] tilt boundary, is also tractable using traditional QM calculations, and serves as a validation for the QM/MM method. The second boundary is a general, low-symmetry tilt boundary that is completely inaccessible to pure QM calculations. QM/MM results for both of these boundaries are used to evaluate the accuracy of empirical (EAM) potentials for the Al-Mg and Al-Pb alloy systems. Based on these results we develop a physical model for the segregation energy based on elastic interaction and bond breaking terms. Both MM calculations with the EAM potentials and the model work quantitatively well for describing Mg-GB interaction across a wide range of local environments. For Pb, MM performance is weaker and the model provides only qualitative insight, demonstrating the utility of a QM/MM approach.