This study presents a facile synthesis of cadmium-free ternary and quaternary quantum dots (QDs) and their application to light-emitting diode (LED) devices. AgInS2 ternary QDs, developed as a substitute for cadmium chalcogenide QDs, exhibited spectrally broad photoluminescence due to intrinsic defect levels. Our group has successfully achieved narrow band-edge PL by a coating with gallium sulfide shell. Subsequently, an intrinsic difficulty in the synthesis of multinary compound QDs, which often results in unnecessary byproducts, was surmounted by a new approach involving the nucleation of silver sulfide followed by material conversion to the intended composition (silver indium gallium sulfide). By fine-tuning this reaction and bringing the starting material closer to stoichiometric compositional ratios, atom economy was further improved. These QDs have been tested in LED applications, but the standard device encountered a significant defective emission that would have been eliminated by the gallium sulfide shells. This problem is addressed by introducing gallium oxide as a new electron transport layer.