We have studied the superconducting gap structure of LaPt$_2$Si$_2$ by measuring the temperature dependence of the London penetration depth shift $Deltalambda(T)$ and point contact spectroscopy of single crystals. $Deltalambda(T)$ shows an exponential temperature dependence at low temperatures, and the derived normalized superfluid density $rho_{s}(T)$ can be well described by a single-gap s-wave model. The point-contact conductance spectra can also be well fitted by an s-wave Blonder-Tinkham-Klapwijk model, where the gap value shows a typical BCS temperature and magnetic field dependence consistent with type-II superconductivity. These results suggest fully gapped superconductivity in LaPt$_2$Si$_2$, with moderately strong electron-phonon coupling.
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