On Least Common Multiples of Polynomials in Z/n Z[x]

Let 𝒫(n, D) be the set of all monic polynomials in ?/n?x] of degree D. A least common multiple for 𝒫(n, D) is a monic polynomial L ∈ ?/n?x] of minimal degree such that f divides L for all f ∈ 𝒫(n, D). A least common multiple for 𝒫(n, D) always exists, but need not be unique; however, its degree is always unique. In this article, we establish some bounds for the degree of a least common multiple for 𝒫(n, D), present constructions for common multiples in ?/n?x], and describe a connection to rings of integer-valued polynomials over matrix rings.