This article considers the problem of several traveling salesmen. The task is to find a set of a predetermined number of disjoint cycles on a graph with weighted arcs, in which the weight (the sum of the weights of the arcs) of the largest cycle is minimal. An accurate algorithm for solving the problem based on the method of branches and boundaries has been developed. The constructed algorithm, as well as the well-known Balas' and Christofides' algorithm for solving the traveling salesman problem, uses the Hungarian algorithm for solving the assignment problem. Numerical experiments with large-dimensional random graphs have been carried out.