The Monte Carlo version of the Modified Glauber Model (MGM)  is updated and applied to the analysis of the total multiplicity yields of charged particles in mucleus-nucleus and proton-nucleus collisions in a broad energy range. The MGM takes into account the energy conservation and momentum loss for particle production in each nucleon-nucleon inelastic collision. This is done by introducing a mean fraction of the initial nucleon momentum which is allowed to be lost in each inelastic interaction between nucleons of colliding nuclei. Therefore, the next nucleon-nucleon inelastic collision takes place at a lower energy √s and with the relevant cross-section sinel(√s). Comparison of theMGMcalculations to the available experimental data on mean total multiplicity <Nch > in central nucleus-nucleus collisions from AGS to RHIC energies allows to fit a single model parameter k = 0.35. The same value of k is found to be valid for successful description of the scaling of < Nch > /2Npart with the number of nucleon-participants Npart in Pb-Pb collisions observed in ALICE at the LHC . A considerable reduction of Ncoll is obtained in MGM for the case of nucleus-nucleus collisions at the LHC energy in comparison with the standard Glauber approach, while the number of participants Npart is practically unchanged. In the MGM approach the nucleon stopping phenomenon is observed, that has dramatic effect in case of proton-nucleus collisions. The MGM predicts considerable decrease (by a factor of about 3 for central collisions in comparison with the standard Glauber-based estimates) of the number of participants < Npart >=< Ncoll > +1 in case of pA interactions at the LHC.