Geodesic
A greatest common divisor identity
The Teaching of Mathematics, XXI (2018) no. 2, p. 73 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
Classification : 97F60 F64
Keywords: Greatest common divisor, fundamental theorem of arithmetic, least common multiple. 
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     author = {Yuanhong Zhi},
     title = {A greatest common divisor identity},
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Yuanhong Zhi. A greatest common divisor identity. The Teaching of Mathematics, XXI (2018) no. 2, p. 73 . http://geodesic.mathdoc.fr/item/TM2_2018_XXI_2_a1/