Abstract Algebra: Theory and Applications · Problem 9.4.54

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-subgroups-lcm

Problem

Let m,n∈Zm, n \in \mathbb{Z}. Prove that ⟨m⟩∩⟨n⟩=⟨l⟩\langle m \rangle \cap \langle n \rangle = \langle l \rangle if and only if l=lcm(m,n)l = \text{lcm}(m, n).

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