The thermal fluctuations contribution to magnetization and magnetoconductivity of type-II layered superconductors is calculated in the framework of the Lawrence-Doniach model. For numerous high-temperature cuprate superconductors, it was discovered that the magnetization dependence on temperature in a wide range of fields exhibits an intersection point at a temperature slightly below Tc. We notice a similar intersection point of the magnetoconductivity curves at the approximate same temperature. The phenomenon is explained by strong (non-Gaussian) thermal fluctuations with interactions treated using a self-consistent theory. All higher Landau levels should be included. Dimensionality of the fluctuations is defined, and the two- to three-dimensional crossover is the key for the existence of intersection points.