We report a measurement of the $D^0$ and $D^+$ lifetimes using $D^0to K^-pi^+$ and $D^+to K^-pi^+pi^+$ decays reconstructed in $e^+e^-to cbar{c}$ data recorded by the Belle II experiment at the SuperKEKB asymmetric-energy $e^+e^-$ collider. The data correspond to an integrated luminosity of $72,{rm fb}^{-1}$. The results, $tau(D^0) = 410.5pm1.1,{rm(stat)}pm0.8,{rm(syst.)},{rm fs}$ and $tau(D^+) = 1030.4pm4.7,{rm(stat)}pm3.1,{rm(syst.)},{rm fs}$, are the most precise to date and are consistent with previous determinations.
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