KöMaL problem A, 2016

Number theory Difficulty 5.0 AIME, harder Prove it Hungary

Let $a_1<a_2<\ldots<a_n$ be an arithmetic progression of positive integers. Prove that $[a_1,a_2,\ldots,a_n] \ge [1,2,\ldots,n]$ . (The symbol $[\ldots]$ stands for the least common multiple.)
(5 pont)

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