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A nice lcm problem

Source: Kvant Magazine No. 1 2024 M2779

April 7, 2024
number theoryLowest common multiple

Problem Statement

Prove that for any natural number kk{} there is a natural number nn{} such that lcm(1,2,…,n)=lcm(1,2,…,n+k).\mathrm{lcm}(1,2,\ldots,n)=\mathrm{lcm}(1,2,\ldots,n+k).
From the folklore
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