In hyperspectral image (HSI) analysis, classification requires spectral dimensionality reduction (DR). While common DR methods use linear algebra, we propose a multilinear algebra method to jointly achieve denoising reduction and DR. Multilinear tools consider HSI data as a whole by processing jointly spatial and spectral ways. The lower rank-(K1, K2, K3) tensor approximation [LRTA-(K1, K2, K3)] was successfully applied to denoise multiway data such as color images. First, we demonstrate that the LRTA-(K1, K2, K3) performs well as a denoising preprocessing to improve classification results. Then, we propose a novel method, referred to as LRTAdr-(K1, K2, D3), which performs both spatial lower rank approximation and spectral DR. The classification algorithm Spectral Angle Mapper is applied to the output of the following three DR and noise reduction methods to compare their efficiency: the proposed LRTAdr-(K1, K2, D3), PCAdr, and PCAdr associated with Wiener filtering or soft shrinkage of wavelet transform coefficients.