  From an examination of ~18,000 Kepler light curves of K- and M-stars we find
some 500 which exhibit rotational periods of less than 2 days. Among such
stars, approximately 50 show two or more incommensurate periodicities. We
discuss the tools that allow us to differentiate between rotational modulation
and other types of light variations, e.g., due to pulsations or binary
modulations. We find that these multiple periodicities are independent of each
other and likely belong to different, but physically bound, stars. This
scenario was checked directly by UKIRT and adaptive optics imaging,
time-resolved Fourier transforms, and pixel-level analysis of the data. Our
result is potentially important for discovering young multiple stellar systems
among rapidly rotating K- and M-dwarfs.
