We present high-resolution observations of a sample of 75 K2 targets from Campaigns 1-3 using speckle interferometry on the Southern Astrophysical Research (SOAR) telescope and adaptive optics (AO) imaging at the Keck II telescope. The median SOAR $I$-band and Keck $K_s$-band detection limits at 1 were $Delta m_{I}=4.4$~mag and $Delta m_{K_s}=6.1$~mag, respectively. This sample includes 37 stars likely to host planets, 32 targets likely to be eclipsing binaries (EBs), and 6 other targets previously labeled as likely planetary false positives. We find nine likely physically bound companion stars within 3 of three candidate transiting exoplanet host stars and six likely EBs. Six of the nine detected companions are new discoveries; one of the six, EPIC 206061524, is associated with a planet candidate. Among the EB candidates, companions were only found near the shortest period ones ($P<3$ days), which is in line with previous results showing high multiplicity near short-period binary stars. This high-resolution data, including both the detected companions and the limits on potential unseen companions, will be useful in future planet vetting and stellar multiplicity rate studies for planets and binaries.
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