Low Temperature Combustion (LTC) engines are promising to improve powertrain fuel economy and reduce NOx and soot emissions by improving the in-cylinder combustion process. However, the narrow operating range of LTC engines limits the use of these engines in conventional powertrains. Extended range electric vehicles (EREVs), by decoupling the engine from the drivetrain, allows the engine to operate in a limited operating range; thus, EREVs offer an ideal platform for realizing the advantages of LTC engines. In this study, the global optimum fuel economy improvement of an experimentally developed 2-liter multi-mode LTC engine in a series EREV is investigated. The engine operation modes include Homogeneous-Charge Compression Ignition (HCCI), Reactivity Controlled Compression Ignition (RCCI), and conventional Spark Ignition (SI). The simulation results show in the city driving cycle, the single-mode HCCI and RCCI engines offer 12% and 9% fuel economy improvement, respectively over a single-mode SI engine in the EREV. These improvements increase to 13.1% and 10.3% in the highway driving cycles. In addition, the mode-switching fuel penalty is included in the optimization problem and the results are used to determine number of LTC modes. The results show that the multi-mode LTC engine offers 2% more fuel economy improvement over the best single-mode LTC engine operation. These results depend on the type of driving cycle and mode-switching fuel penalty. HCCI and RCCI engine modes can be the dominant optimal engine operating modes depending on the mode-switching fuel penalty value.