Synchronized Pulse

You are monitoring K scientific sensors. Each sensor i produces a pulse starting at time T_i and repeats every P_i milliseconds (i.e., at T_i, T_i + P_i, T_i + 2P_i, ...). All pulses are recorded in a single global timeline. Find the time of the M-th pulse to occur across all sensors. (Note: Pulses at the same time are counted separately). Example: K=2 sensors, M=3 pulses. Sensor 0: Start 5, Period 10 (Pulses: 5, 15, 25...) Sensor 1: Start 7, Period 5 (Pulses: 7, 12, 17...) Timeline: 5, 7, 12, 15, 17... 3rd pulse is at time 12.