A new speed enhancement technique for pulsed laser rangefinders based on Lagrange's theorem in group theory using an undersampling method has been developed. In the undersampling method, frequency conversion for high-resolution ranging and digitizing are conducted by sampling a reference frequency signal at the timings of the reception of pulsed light from the target. In the present work, the rangefinder generates different sampling intervals of the reference frequency signal: different numbers of sampling points within the period of a reference signal, over a wide range. This is accomplished by slightly changing the period of the pulsed light emitted, without changing the synthesizer frequency which generates the period. This technique requires a minimum of additional hardware. In this paper, we describe the detail of the selection of the number of sampling points based on Lagrange's theorem. And we demonstrate a possibility of expanding the sampling interval to the point where an aliasing of the harmonic components of the reference signal occurs by simulations that focus on the calculation of the phase of the fundamental frequency of the reference signal. And we report on the results of rangefinder experiments for a reduction in the number of the sampling points. We have achieved a 10-fold enhancement of speed by selecting 10 sampling points over the results from the previous studies that had 100 sampling points within a period of a reference signal. And we have confirmed that the reduction in sampling points has a very little influence on the linearity, which is an acceptable trade-off for achieving the speed enhancement. This technique, based on Lagrange's theorem in group theory, allows us to control the minimum number of samplings required to calculate distances, so that high-speed data acquisition for coarse measurements and normal-speed data acquisition for fine measurements become selectable. Such a system with high flexibility in measurement modes has been developed.