  Recently, the discovery of room-temperature superconductivity (SC) was
experimentally realized in the fcc phase of LaH$_{10}$ under megabar pressure.
Specifically, the isotope effect of $T_{\rm c}$ was measured by the replacement
of hydrogen (H) with deuterium (D), demonstrating a driving role of phonons in
the observed room-temperature SC. Herein, based on the first-principles
calculations within the harmonic approximation, we reveal that (i) the
identical electron-phonon coupling constants of fcc LaH$_{10}$ and LaD$_{10}$
decrease monotonously with increasing pressure and (ii) the isotope effect of
$T_{\rm c}$ is nearly proportional to $M^{-{\alpha}}$ ($M$: ionic mass) with
${\alpha}$ ${\approx}$ 0.465, irrespective of pressure. The predicted value of
${\alpha}$ agrees well with the experimental one (${\alpha}=0.46$) measured at
around 150 GPa. Thus, our findings provide a theoretical confirmation of the
conventional electron-phonon coupling mechanism in a newly discovered
room-temperature superconductor of compressed LaH$_{10}$.
