Let $n_1,n_1,\ldots,n_k\in\mathbb Z$ be integers. The simultanous least common multiple of all these numbers can be calculated by the recursive formula
$$\operatorname{lcm}(n_1,\ldots,n_k):=\operatorname{lcm}(\operatorname{lcm}(n_1,\ldots,n_{k-1}),n_k).$$
This calculation is independent of the order, in which the recursive formula is used, following the associativity and commutativity of the $\operatorname{lcm}$. In particular, for any integers $a,b,c\in\mathbb Z$ we have $$\operatorname{lcm}(\operatorname{lcm}(a,b),c))=\operatorname{lcm}(a,\gcd(b,c))$$ and $$\operatorname{lcm}(a,b)=\operatorname{lcm}(b,a).$$
Proofs: 1
Proofs: 1
Propositions: 2
Theorems: 3