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 oscil-Ⅲ lations 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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