The temperature dependence of the resistivity and magnetic moment of La0.85Ba0.15MnO3 and La0.85Sr0.15MnO3 manganite single crystals in magnetic fields up to 90 kOe is investigated. Analysis of the experimental results shows that the magnetoresistance of lanthanum manganites far from the Curie temperature TC can be described quantitatively by the s-d model normally used for ferromagnets and taking into account only the exchange interaction between the spins of charge carriers and magnetic moments. These data also show that the features of lanthanum manganites responsible for colossal magnetoresistance (CMR) are manifested in a narrow temperature interval δT ≈ 20 K near TC. Our results suggest a CMR mechanism analogous to the mechanism of giant magnetoresistance (GMR) observed in Fe/Cr-type multilayers with nanometer layer thickness. The nanostratification observed in lanthanum manganites and required for GMR can be described taking into account the spread in TC in the CMR range δT.