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This paper proposes a simple and effective modification of the conventional divide-by-two injection locked frequency divider (ILFD) with direct-injection aimed at allowing both the divide-by-two and the divide-by-three modes of operation. The proposed circuit does not employ additional inductors as usual in divide-by-three ILFDs, but exploits the combined effect of two independent injection techniques. The resulting locking range for the divide-by-three mode is comparable in size to that for the divide-by-two. Thus, the proposed circuit can be an optimum alternative to existing dividers, due to the flexibility of two division ratios and due to the absence of additional inductors. An intuitive explanation of the locking mechanism underlying this ILFD and a quantitative analysis are provided, allowing one to predict the amplitude and phase of oscillation in the locked mode, as well as the locking range, with approximate closed-form expressions. Measurements on a circuit prototype and results from SPICE simulations demonstrate the effectiveness of the circuit and validate the theoretical model and the resulting formulas.