  In this paper, we study some of the factorization aspects of rational
multicyclic monoids, that is, additive submonoids of the nonnegative rational
numbers generated by multiple geometric sequences. In particular, we provide a
complete description of the rational multicyclic monoids $M$ that are
hereditarily atomic (i.e., every submonoid of $M$ is atomic). Additionally, we
show that the sets of lengths of certain rational multicyclic monoids are
finite unions of multidimensional arithmetic progressions, while their unions
satisfy the Structure Theorem for Unions of Sets of Lengths. Finally, we
realize arithmetic progressions as the sets of distances of some additive
submonoids of the nonnegative rational numbers.
