We compute the strange quark mass $m_s$ and the average of the $u$ and $d$ quark masses $hat m$ using full lattice QCD with three dynamical quarks combined with experimental values for the pion and kaon masses. The simulations have degenerate $u$ and $d$ quarks with masses $m_u=m_dequiv hat m$ as low as $m_s/8$, and two different values of the lattice spacing. The bare lattice quark masses obtained are converted to the $msbar$ scheme using perturbation theory at $O(alpha_s)$. Our results are: $m_s^msbar$(2 GeV) = 76(0)(3)(7)(0) MeV, $hat m^msbar$(2 GeV) = 2.8(0)(1)(3)(0) MeV and $m_s/hat m$ = 27.4(1)(4)(0)(1), where the errors are from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.
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