The electronic structure of Pd-3 and Pt-3 clusters and the detailed reaction mechanism of activation of H-2 and CH4 on these clusters have been studied with a density functional method. Full geometry optimization has been carried out and led to the reaction mechanisms that are dramatically different from those of a previous work where only limited potential energy scans were carried out. In the Pd-3 + H-2 system, Pd-3, like Pd-2, activates H-2 without barrier. For the activation of the C-H bond in CH4 with Pd-3, although the final products are found to be similar in energy compared to the case of Pd-2, the activation barriers on Pd-3 are much higher than those on Pd-2. This difference has been explained in terms of the large repulsion from the s(1)d(9) configurations of Pd atoms in Pd-3, whereas Pd atoms in Pd-2 adopt mainly the less repulsive d(10) configuration. In the case of Pt-3 + H-2/CH4, the reactions basically follow the same pattern as in the Pt-2 systems. Namely H-H and C-H are broken at first on a single Pt atom, and then one H atom migrates to other Pt atom(s). No activation barrier has been found on either the singlet or the triplet state for H-H activation, and a smaller activation barrier height compared to the Pt-2 case has been obtained for the C-H activation. Results from the current series of studies are consistent with the recent experimental observations on the reactivities of unsupported Pd-n and Pt-n.