It is well established that stellar rotation is dependent on age and mass for single and widely separated binary systems of M Dwarfs (stars 10-60% the mass of our Sun). However, about a quarter of M Dwarfs have stellar companions, most of which are closer than 50 times the Sun to Earth distance. We know less about these systems due to challenges in their analysis. A remaining question is whether there is a separation where these dependencies no longer hold. Thus, it is important to determine rotation periods for stars in binary systems.

We analyzed Transiting Exoplanet Survey Satellite (TESS) light curves for M-dwarf binaries GJ 896AB (20.2LY) and LSPM J2240-4031AB (38.8LY). We detected two rotation periods for each system but were unable to match them to their stellar components from TESS data alone due to the large pixels on the TESS cameras. Because these systems are resolvable at ground-based facilities, we used the Cerro Tololo Inter-American Observatory (CTIO) 0.9m telescope to obtain photometric data. We performed relative photometry to match period detections to their sources. We also analyzed rotational broadening measurements from high-resolution spectrographs. For GJ 896AB, we determined rotation periods of 1.07 and 0.40 days for the primary star and companion respectively. For LSPM J2240-4931AB, we are still unable to determine which rotation period corresponds to which star. Our results add to our growing understanding of rotation periods in M-dwarf binary systems.