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prove [k,m] [m,n] [n,k] >= [k,m,n]^2 for any natural numbers k,m,n

Source: All Russian MO 1994 ARO

July 29, 2018
least common multipleInequalitynumber theory

Problem Statement

Prove that, for any natural numbers k,m,nk,m,n: [k,m]⋅[m,n]⋅[n,k]≥[k,m,n]2[k,m] \cdot [m,n] \cdot [n,k] \ge [k,m,n]^2
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