A novel and useful apparatus for and method of local oscillator (LO) generation with non-integer multiplication ratio between the local oscillator and RF frequencies. The LO generation schemes presented are operative to generate I and Q square waves at a designated frequency while avoiding the well known issue of harmonic pulling. The input signal is fed to a synthesizer timed to a rational multiplier of the RF frequency L/N fRF. The clock signal generated is divided by a factor Q to form 2Q phases of the clock at a frequency of L(N*Q)fRF, wherein each phase undergoes division by L. The phase signals are input to a pulse generator which outputs a plurality of pulses. The pulses are input to a selector which selects which signal to output at any point in time. By controlling the selector, the output clock is generated as a TDM based signal. Any spurs are removed by an optional filter.