A systematic study of RR Lyrae stars is performed using a selected sample of 655 objects in the Large Magellanic Cloud (LMC) with long-term observations and numerous measurements from the Optical Gravitational Lensing Experiment III project. The phase dispersion method and linear superposition of the harmonic oscillations are used to derive the pulsation frequency and properties of light variation. It is found that a dichotomy exists in Oosterhoff Type I and Oosterhoff Type II for RR Lyrae stars in the LMC. Due to our strict criteria for identifying a frequency, a lower limit for the incidence rate of Blazhko modulation in the LMC is estimated in various subclasses of RR Lyrae stars. For fundamental-mode RR Lyrae stars, the rate of 7.5% is smaller than the previous result. In the case of the first-overtone RR Lyrae variables, the rate of 9.1% is relatively high. In addition to the Blazhko variables, 15 objects are identified to pulsate in the fundamental/first-overtone double mode. Furthermore, four objects show a period ratio around 0.6, which makes them very likely to be rare pulsators in the fundamental/second-overtone double mode.

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