  Experiments at the Large Hadron Collider (LHC) have measured multiplicity
distributions in p+p and p+Pb collisions at a new domain of collision energy.
Based on considering an energy-dependent broadening of the nucleon's density
distribution, charged hadron multiplicities are studied with the
phenomenological saturation model and the evolution equation dependent
saturation model. By assuming the saturation scale have a small dependence on
the 3-dimensional root mean square (rms) radius at different energy, the
theoretical results are in good agreement with the experimental data from CMS
and ALICE collaboration. Then, the predictive results in p+p collisions at
$\sqrt{s}=$ 14 TeV of the LHC are also given.
