We show, both experimentally and theoretically, that a slave laser injected with an optical frequency comb can undergo two distinct locking mechanisms, both of which decrease the output optical comb's frequency spacing. We report that, for certain detuning and relative injection strengths, slave laser relaxation oscillations can become undamped and lock to rational frequencies of the optical comb spacing, creating extra comb tones by nonlinear dynamics of the injected laser. We also study the frequency locking of the slave laser at detunings in between the injected comb lines, which add the slave laser's frequency to the comb. Our results demonstrate the effect of the α parameter and stability of the locked states and indicate how the frequency of the relaxation oscillations affect both of these locking mechanisms. These optical locking mechanisms can be applied to regenerate or multiply optical combs.