The momentum and temperature dependence of the superconducting gap and pseudogap in optimally-doped Bi$_2$Sr$_{1.6}$La$_{0.4}$CuO$_6$ superconductor is investigated by super-high resolution laser-based angle-resolved photoemission spectroscopy. The measured energy gap in the superconducting state exhibits a standard {it d}-wave form. Pseudogap opens above T$_c$ over a large portion of the Fermi surface with a Fermi arc formed near the nodal region. In the region outside of the Fermi arc, the pseudogap has the similar magnitude and momentum dependence as the gap in the superconducting state which changes little with temperature and shows no abrupt change across T$_c$. These observations indicate that the pseudogap and superconducting gap are closely related and favor the picture that the pseudogap is a precursor to the superconducting gap.