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.

Keywords: Greatest common divisor; fundamental theorem of arithmetic; least common multiple.

Pages:  73$-$79     

Volume  XXI ,  Issue  2 ,  2018