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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 quarkscombined with experimental values for the pion and kaon masses. The simulationshave degenerate $u$ and $d$ quarks with masses $m_u=m_d\equiv \hat m$ as low as$m_s/8$, and two different values of the lattice spacing. The bare latticequark masses obtained are converted to the $\msbar$ scheme using perturbationtheory 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.Comment: 5 pages, revtex, 2 figures. v2: New ms/hat(m) discussion and  reference, v3: slight change in discussion of referenc

First determination of the strange and light quark masses from full lattice QCD