A method is described for calculating the magnetotransport properties of a two-component composite conducting medium which has a periodic microstructure. The method is based on a Fourier series expansion of the local electric potential. Because a large number of expansion coefficients needs to be used in order to get reliable results for the bulk effective behavior, a special approach is developed that does not require solving a large set of coupled linear algebraic equations for them. Results are presented for the magnetoresistance and Hall resistance as functions of the magnetic field in a number of models where periodic arrays of insulating inclusions of various shapes are embedded in a uniform host material. These samples include cases where the inclusions are well separated as well as cases where they touch and where they overlap.