We investigate theoretically productions of Λ3,4H bound states in the exothermic (K−, π0) reactions on 3,4He targets at pK−= 1.0 GeV/c in a distorted-wave impulse approximation with the optimal Fermi-averaging K−p→π0Λt matrix. We calculate angular distributions of the laboratory differential cross sections dσ/dΩlab and the integrated cross sections σlab for a JP=0+ ground state and a JP=1+ excited state of HΛ4 at π0 forward-direction angles of θlab= 0∘–20∘, and those for a JP=1/2+ ground state of HΛ3. The production of a JP=3/2+ excited state of HΛ3 as a virtual state is also evaluated. The comparison in dσ/dΩlab and σlab between HΛ4 and HΛ3 provides examining the mechanism of the production and structure of Λ3,4H, as well as in the endothermic (π−, K0) reactions at pπ−= 1.05 GeV/c. This investigation confirms the feasibility of lifetime measurements of Λ3H at the J-PARC experiments.