Least Mean Square (LMS) algorithm is the most used adaptive filter for digital signal processing. Able to adapt its impulse response following external solicitations, it requires a huge number of multipliers for coefficients updating. Therefore, power consumption issues arise. In this paper, the precision of input signal in the update section is dynamically scaled with a variable rounding according to the magnitude of the error signal absolute value, thus allowing the switching activity reduction in multipliers. Implementation in TSMC 28 nm CMOS technology reveals a power saving up to 27% with respect to a standard LMS with negligible performances degradation.