We investigate the intrinsic Gilbert damping constant in perpendicular magnetic anisotropy Co/Ni multilayer system by means of an all-optical method. We find that the intrinsic Gilbert damping constant does not depend on the stack number and the perpendicular magnetic anisotropy when the magnetic field is high enough. In contrast, the extrinsic Gilbert damping is strongly correlated with the inhomogeneous anisotropy distribution in the low-field regime, as observed in magneto-optical images. Intriguingly, the extrinsic Gilbert damping is consistently reduced with decreasing length scale in the measurements, providing a concrete means to determine the intrinsic Gilbert damping.