This paper proposes an axiomatic solution to the problem of choice of the dynamic construction of prices and quantities indices and trajectories. There has been proved the existence of prices and quantities paths which are identical to those generating Divisia and Montgomery indices. The obtained Divisia – Montgomery indices (also known as log-change or Montgomery – Vartia(I) index numbers) possess the axiomatic properties of both Montgomery and Divisia indices and are recommended for practical application. They are uniquely characterized by a constant on the trajectories and equal shares of each factor’s contribution to value change and to logarithm of the index value for a given set of goods. This indices’ property corresponds to the statistical practice’s assumption of homogeneity of the studied process of combined changes in prices and quantities in the neighboring periods. The proposed approach could be extended to the calculation of chain indices for the sequences of the compared states-periods.