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In this work we calculate the effects of quantum fluctuations in two kinds of topological skyrmions textures on the triangular lattice by means of the Holstein-Primakoff approximation. In the first case we consider a "standard" skyrmion lattice on the ferromagnetic  Heisenberg model with Dzyalonshinkii-Moriya interactions, chosen so that the classical ground state displays a skyrmion crystal (SkX). In the second case, we consider an antiferromagnetic model where the magnetic frustration induces an antiferromagnetic skyrmion crystal (AF-SkX). Here, the AF-SkX state consists of three interpenetrating Skyrmion crystals (one by sublattice) having important consequences in the spectrum of Spin-waves. In both cases, we discuss the magnon bands, zero-point energy and the magnon distribution density.