$TiO_2$- and $SiO_2$-supported $Co_3O_4$, Pt and $Co_3O_4$-Pt catalysts have been studied for CO and $C_3H_8$ oxidations at temperatures less than $250^{circ}C$ which is a lower limit of light-off temperatures to oxidize them during emission test cycles of gasoline-fueled automotives with TWCs (three-way catalytic converters) consisting mainly of Pt, Pd and Rh. All the catalysts after appropriate activation such as calcination at $350^{circ}C$ and reduction at $400^{circ}C$ exhibited significant dependence on both their preparation techniques and supports upon CO oxidation at chosen temperatures. A Pt/$TiO_2$ catalyst prepared by using an ion-exchange method (IE) has much better activity for such CO oxidation because of smaller Pt nanoparticles, compared to a supported Pt obtained via an incipient wetness (IW). Supported $Co_3O_4$-only catalysts are very active for CO oxidation even at $100^{circ}C$, but the use of $TiO_2$ as a support and the IW technique give the best performances. These effects on supports and preparation methods were indicated for $Co_3O_4$-Pt catalysts. Based on activity profiles of CO oxidation at $100^{circ}C$ over a physical mixture of supported Pt and $Co_3O_4$ after activation under different conditions, and typical light-off temperatures of CO and unburned hydrocarbons in common TWCs as tested for $C_3H_8$ oxidation at $250^{circ}C$ with a Pt-exchanged $SiO_2$ catalyst, this study may offer an useful approach to substitute $Co_3O_4$ for a part of platinum group metals, particularly Pt, thereby lowering the usage of the precious metals.