# 2018-08 Large LCM

Let $$a_1$$, $$a_2$$, $$\ldots$$, $$a_m$$ be distinct positive integers. Prove that if $$m>2\sqrt{N}$$, then there exist $$i$$, $$j$$ such that the least common multiple of $$a_i$$ and $$a_j$$ is greater than $$N$$.

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