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We present results of magnetic torque calculations using the fully relativistic spin-polarized Korringa-Kohn-Rostoker approach applied to small Co and Fe clusters deposited on the Pt(111) surface. From the magnetic torque one can derive amongst others the magnetic anisotropy energy (MAE). It was found that this approach is numerically much more stable and also computationally less demanding than using the magnetic force theorem that allows to calculate the MAE directly. Although structural relaxation effects were not included our results correspond reasonably well to recent experimental data.