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In this paper, we study some of the factorization aspects of rationalmulticyclic monoids, that is, additive submonoids of the nonnegative rationalnumbers generated by multiple geometric sequences. In particular, we provide acomplete description of the rational multicyclic monoids $M$ that arehereditarily atomic (i.e., every submonoid of $M$ is atomic). Additionally, weshow that the sets of lengths of certain rational multicyclic monoids arefinite unions of multidimensional arithmetic progressions, while their unionssatisfy the Structure Theorem for Unions of Sets of Lengths. Finally, werealize arithmetic progressions as the sets of distances of some additivesubmonoids of the nonnegative rational numbers.

On the sets of lengths of Puiseux monoids generated by multiple geometric sequences