Differential cross sections and photon beam asymmetries for the gamma p rightarrow K+ Lambda and gamma p rightarrow K+ Sigma0 reactions have been measured in the photon energy range from 1.5 GeV to 2.4 GeV and in the angular range from Theta_{cm} = 0 to 60 of the K+ scattering angle in the center of mass system at the SPring-8/LEPS facility. The photon beam asymmetries for both the reactions have been found to be positive and to increase with the photon energy. The measured differential cross sections agree with the data measured by the CLAS collaboration at cosTheta_{cm}<0.9 within the experimental uncertainties, but the discrepancy with the SAPHIR data for the K+Lambda reaction is large at cosTheta_{cm}>0.9. In the K+Lambda reaction, the resonance-like structure found in the CLAS and SAPHIR data at W=1.96 GeV is confirmed. The differential cross sections at forward angles suggest a strong K-exchange contribution in the t-channel for the K+Lambda reaction, but not for the K+Sigma0 reaction.
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