MathDB
A 68

Source:

May 25, 2007
number theoryleast common multiplegreatest common divisorDivisibility Theory

Problem Statement

Suppose that S={a1,⋯ ,ar}S=\{a_{1}, \cdots, a_{r}\} is a set of positive integers, and let SkS_{k} denote the set of subsets of SS with kk elements. Show that lcm(a1,⋯ ,ar)=∏i=1r∏s∈Sigcd⁡(s)((−1)i).\text{lcm}(a_{1}, \cdots, a_{r})=\prod_{i=1}^{r}\prod_{s\in S_{i}}\gcd(s)^{\left((-1)^{i}\right)}.
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