We use the renormalization-group equations to calculate the symmetry-breaking scales in the [SU(6)${]}^{3}$ Pati-Salam model. Using only known parameters, we predict the mass scales consistent with very small values for the light-neutrino masses and rare processes decay such as ${\mathit{K}}^{+}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\mu}}}^{+}$ for three steps of symmetry breaking. We also find that the proton is stable by gauge and Higgs boson exchange.