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Multijet production rates in neutral current deep inelastic scattering havebeen measured in the range of exchanged boson virtualities 10 < Q2 < 5000 GeV2.The data were taken at the ep collider HERA with centre-of-mass energy sqrt(s)= 318 GeV using the ZEUS detector and correspond to an integrated luminosity of82.2 pb-1. Jets were identified in the Breit frame using the k_T clusteralgorithm in the longitudinally invariant inclusive mode. Measurements ofdifferential dijet and trijet cross sections are presented as functions of jettransverse energy E_{T,B}{jet}, pseudorapidity eta_{LAB}{jet} and Q2 withE_{T,B}{jet} > 5 GeV and -1 < eta_{LAB}{jet} < 2.5. Next-to-leading-order QCDcalculations describe the data well. The value of the strong coupling constantalpha_s(M_Z), determined from the ratio of the trijet to dijet cross sections,is alpha_s(M_Z) = 0.1179 pm 0.0013(stat.) {+0.0028}_{-0.0046}(exp.){+0.0064}_{-0.0046}(th.)Comment: 22 pages, 5 figure

Multijet production in neutral current deep inelastic scattering at HERA and determination of $\alpha_s$