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We demonstrate a tunable passive all-optical pulse repetition rate multiplier based on the fractional temporal Talbot effect. The multiplier comprises a series of identical linearly chirped fiber Bragg gratings (LCFBGs) interconnected via two multiport (N×N) switches. Discrete multiplication factors are obtained by simply using the switch to set the optical path of the input pulse train to be reflected by the required number of gratings, and hence, corresponding dispersion, to satisfy the Talbot condition. In our demonstration, we reflect an 8.62-GHz input pulse train from a cascade of one to four LCFBGs, resulting in discrete repetition rate multiplication factors of 12, 6, 4, and 3, respectively. We obtain output repetition rates exceeding 100 GHz; the multiplied train exhibits excellent signal stability with low amplitude ripple and timing jitter, and the output pulses are of similar duration to those at the input.