  The pseudorapidity distributions of charged hadrons in proton-lead collisions
at nucleon-nucleon center-of-mass energies $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 and
8.16 TeV are presented. The measurements are based on data samples collected by
the CMS experiment at the LHC. The number of primary charged hadrons produced
in non-single-diffractive proton-lead collisions is determined in the
pseudorapidity range $|\eta_\mathrm{lab}| <$ 2.4. The charged-hadron
multiplicity distributions are compared to the predictions from theoretical
calculations and Monte Carlo event generators. In the center-of-mass
pseudorapidity range $|\eta_\mathrm{cm}| < 0.5$, the average charged-hadron
multiplicity densities
$<\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta_{\mathrm{cm}}>$$\vert_{|\eta_{\mathrm{cm}}|
< 0.5}$ are 17.31 $\pm$ 0.01 (stat) $\pm$ 0.59 (syst) and 20.10 $\pm$ 0.01
(stat) $\pm$ 0.85 (syst) at $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 and 8.16 TeV,
respectively. The particle densities per participant nucleon are compared to
similar measurements in proton-proton, proton-nucleus, and nucleus-nucleus
collisions.
