  A systematic study of RR Lyrae stars is performed based on a selected sample
of 655 objects in the Large Magellanic Cloud with observation of long span and
numerous measurements by 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 variation
properties. It is found that there exists an Oo I and Oo II dichotomy in the
LMC RR Lyrae stars. Due to our strict criteria to identify a frequency, a lower
limit of the incidence rate of Blazhko modulation in LMC is estimated in
various subclasses of RR Lyrae stars. For fundamental-mode RR Lyrae stars, the
rate 7.5% is smaller than previous result. In the case of the first-overtone RR
Lyr variables, the rate 9.1% is relatively high. In addition to the Blazhko
variables, fifteen 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 the rare pulsators in the
fundamental/second-overtone double-mode.
