Abstract In this paper, we present an identity involving the greatest common
divisors of almost all possible subproducts of $n$ nonzero
integers. Then we prove this identity, with the help of the
fundamental theorem of arithmetic, and an identity concerning the
minimum function $\min$. As a consequence, a new formula for the
least common multiple is derived. ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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