We investigate the conductance and giant magnetoresistance (GMR) in the current perpendicular-to-the-plane geometry in magnetic multilayers via a third-nearest-neighbor tight-binding model with s, p, and d orbitals. An iterative method is used to calculate the Green's function of the multilayer. The conductance, due to both minority and majority spin channels, is calculated in the ferromagnetic and antiferromagnetic configurations using the Landauer-Büttiker formula. Oscillations of GMR, both with spacer and magnetic layer thicknesses, are observed and the contributions to the conductance due to various extremal points on the Fermi surface are studied. Ballistic conductance and GMR are found to saturate very fast with the number of periods in the multilayer.