We report on the successful demonstration of second and third harmonic conversion of a high pulse energy, high average power 1030 nm diode pumped Yb-doped yttrium aluminum garnet (Yb:YAG) nanosecond pulsed laser in a large aperture lithium triborate (LBO) crystal. We demonstrated generation of 59.7 J at 10 Hz (597 W) at 515 nm (second harmonic) and of 65.0 J at 1 Hz (65 W) at 343 nm (third harmonic), with efficiencies of 66% and 68%, respectively. These results, to the best of our knowledge, represent the highest energy and power reported for frequency conversion to green and UV-A wavelengths.