Local coercivity variation of Co/Pd nanomultilayers has been investigated by measuring the polar Kerr hysteresis loops of local areas of submicron size using a magnetooptic Kerr microscope system. Interestingly, the local coercivity distribution is very sensitive to an increase in the number of repeats: the $(2-{AA};Co/ll-{AA} Pd)_10$ sample showed a smooth variation of the local coercivity, while $(2-{AA};Co/ll-{AA} Pd)_18$ showed a large fluctuation. From micromagnetic considerations based on a thermally activated relaxation odel, we have found that this local coercivity variation has a crucial effect on the contrasting magnetization reversal behavior observed in those samples: dominant wall-motion far the former sample and dominant nucleation for the latter one.