We demonstrate how the interplay of a future e^+e^- LC at its first stage with sqrt{s} sim 500 GeV and of the LHC could lead to a precise determination of the fundamental SUSY parameters in the gaugino/higgsino sector without assuming a specific supersymmetry breaking scheme. We demonstrate this for the benchmark scenario SPS1a, taking into account realistic errors for the masses and cross sections measured at the LC with polarised beams, including errors coming from polarisation measurements, and mass measurements at the LHC. The results clearly demonstrate the complementarity of the LHC and LC, and the benefit from the joint analyses of their data.