We report measurements of the lifetimes of the $Lambda_c^+$, $Xi_c^+$ and $Xi_c^0$ charm baryons using proton-proton collision data at center-of-mass energies of 7 and 8tev, corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected by the LHCb experiment. The charm baryons are reconstructed through the decays $Lambda_c^+to pK^-pi^+$, $Xi_c^+to pK^-pi^+$ and $Xi_c^0to pK^-K^-pi^+$, and originate from semimuonic decays of beauty baryons. The lifetimes are measured relative to that of the $D^+$ meson, and are determined to be begin{align*} tau_{Lambda_c^+} &= 203.5pm1.0pm1.3pm1.4~{rm fs}, ewline tau_{Xi_c^+} &= 456.8pm3.5pm2.9pm3.1~{rm fs}, ewline tau_{Xi_c^0} &= 154.5pm1.7pm1.6pm1.0~{rm fs}, end{align*} where the uncertainties are statistical, systematic, and due to the uncertainty in the $D^+$ lifetime. The measurements are approximately 3--4 times more precise than the current world average values. The $Lambda_c^+$ and $Xi_c^+$ lifetimes are in agreement with previous measurements; however, the $Xi_c^0$ baryon lifetime is approximately 3.3 standard deviations larger than the world average value.
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