IMO 1972 LL SWE38

Congruent rectangles with sides m (cm) and n (cm) are

IMO 1972 LL SWE38

Origin: SWE

Problem

Congruent rectangles with sides m (cm) and n (cm) are given (m, n positive integers). Characterize the rectangles that can be constructed from these rectangles (in the fashion of a jigsaw puzzle). (The number of rectangles is unbounded.)