Low-noise repetition-rate multiplication of optical pulses is demonstrated through harmonic injection locking of a mode-locked laser and gain-saturated amplification by a semi-conductor optical amplifier (SOA). The approach employs strong optical injection for lowering the repetition-rate phase noise, followed by gain-saturated SOA for suppression of pulse intensity irregularities. In this way, we can achieve low phase noise level and high side-mode suppression ratio (SMSR) at the same time. Experimentally, we show repetition-rate multiplication of a 250-MHz commercial mode-locked laser to 1-GHz repetition-rate, with 3% modulation depth, 33-dB SMSR, and 14-fs absolute rms timing jitter (when integrated from 10 kHz to 10 MHz offset frequency).