Laser-induced plasma ignition and assisted combustion of premixed methane/air flames are investigated using a repetitive nanosecond Nd:YAG laser. The flame kernels formed in the ignition process break up into two sub-kernels, which results from the hydrodynamic stretch induced by the toroidal structures generated in the breakdown process. The flame propagation speeds of the upper and lower fronts of the flame kernels are enhanced under low flow speed conditions. Faster propagation of the upper fronts than the lower fronts enables the catch-up of consecutive flame kernels and flameholding using high repetition laser-induced plasmas. The laser repetition rate (f(rep)) to realize cost-effective flameholding is determined from the temporal propagation of the flame fronts. The minimum frep to achieve flameholding at 1-5 mm above the plasma are 387-534 Hz, 454-612 Hz, and 610-869 Hz for the flows of 5.5 m/s, 6.3 m/s, and 9.0 m/s, respectively, and the corresponding up limits for the frep are 704 Hz, 775 Hz, and 1030 Hz, respectively.