The effect of thermal and quantum fluctuations of vortices on the reversible magnetization in the mixed state in highly anisotropic layered superconductors is discussed. For a magnetization, M, a change of slope in the M vs In B curves below 70 K, observed in Bi-2:2:1:2 and Tl-2:2:0:1 single crystals, is explained by quantum fluctuations of vortices within the Lawrence-Doniach model which incorporates viscous dynamics of pancake vortices.