A system is provided having a multiplexed laser source which combines the outputs of multiple lasers into multiplexed illumination which is then externally modulated to provide output illumination having reduced or zero speckle. Each of the laser sources are turned ON and OFF (gated) in a timed sequence to provide multiplexed illumination having a time-averaged speckle contrast that is lesser than the speckle contrast of the output of any one of the lasers. The output of one or more lasers may also be wavelength multiplexed, where the lasers operate at different wavelengths, and/or polarization multiplexed. An external modulator receives and modulates the multiplexed output in phase and/or modal power distribution to further reduce the speckle in the output of the system. The multiplexed laser source and external modulator can be used as separate apparatuses for reducing speckle in laser illumination.