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We present a low-coherent interferometric system of multiplexed sensors based on pairs of long-period gratings (LPGs). The LPGs in each pair have approximately 3-dB transitivity and form an in-fiber Mach-Zehnder interferometer. By using a dual-beam Michelson interferometer with two reflective mirrors, the interferometric signature of the LPG pair is obtained fast and accurately by scanning one of the mirrors. For multiple sensors, their center-to-center grating intervals are preset to be discrete with specific spacing, which ensures the interferometric signatures are separated for simultaneous demodulation. A measurement of bending is demonstrated to verify good performances of the system in terms of low crosstalk and high sensitivity.