Numerical semigroups have long been studied for their interesting algebraic properties. Given a numerical semigroup and , the collection of arithmetic sequences with step size contained in naturally forms a monoid, denoted as . We refer to these monoids as Leamer monoids. These monoids were originally constructed to study special cases of the Huneke-Wiegand conjecture. We provide foundational results for the factorization theory of Leamer monoids, including a full description of their elasticities. We also give a complete description of the Leamer monoid when is generated by an arithmetic sequence with step size . We also study the collections of numerical semigroups which generate the same Leamer Monoid.