The 27-level cascaded multilevel inverter (CMLI) is a popular CMLI, since it can produce an output voltage with nearly sinusoidal wave form and may be realized as a trinary asymmetric CMLI that consists of only three H-bridges. A new approach using a mixed integer linear programming (MILP) model is applied, that can determine the switching angles of this CMLI that minimize the values of any undesired harmonics. The model is applied first to determine the number of harmonics to be minimized to obtain least percentage total harmonic distortion (%THD) utilizing the 13 positive levels of the inverter. The obtained result is then included in the model and it is solved for different values of the output voltage. Single phase and three phase cases are investigated. The results show very low values of %THD and low order harmonics over wide voltage range till the 91st harmonic in both cases, which agree with the IEEE standards 519-1992 for voltage distortion limits till 161 kv.