Through the introduction of multi-frequency sonication in High Intensity Focused Ultrasound (HIFU), enhancement of efficiency has been noted in several applications including thrombolysis, tissue ablation, sonochemistry, and sonoluminescence. One key experimental observation is that multi-frequency ultrasound can help lower the inertial cavitation threshold, thereby improving the power efficiency. However, this has not been well corroborated by the theory. In this paper, a numerical investigation on the inertial cavitation threshold of microbubbles (MBs) under multi-frequency ultrasound irradiation is conducted. The relationships between the cavitation threshold and MB size at various frequencies and in different media are investigated. The results of single-, dual and triple frequency sonication show reduced inertial cavitation thresholds by introducing additional frequencies which is consistent with previous experimental work. In addition, no significant difference is observed between dual frequency sonication with various frequency differences or power allocations on the two frequencies. This study, not only reaffirms the benefit of using multi-frequency ultrasound for various applications, but also provides a possible route for optimizing ultrasound excitations for initiating inertial cavitation.