This paper develops a homogeneity-based approach to finite/fixed-time stabilization of a linear time-invariant (LTI) system with quantized measurements. A sufficient condition for finite/fixed-time stabilization of multi-input LTI system under state quantization is derived. It is shown that a homogeneous state feedback with a novel logarithmic-like quantizer design can guarantee finite/fixed-time stability of the closed-loop system, provided that the quantization is sufficiently dense. Theoretical results are supported with numerical simulations.