Lowest Common Multiple/Examples/n and n+1

Example of Lowest Common Multiple of Integers
Let $n \in \Z_{>0}$ be a strictly positive integer. The lowest common multiple of $n$ and $n + 1$ is:
 * $\lcm \set {n, n + 1} = n \paren {n + 1}$

Proof
We find the greatest common divisor of $n$ and $n + 1$ using the Euclidean Algorithm:

Thus $\gcd \set {n, n + 1} = 1$.

Hence by definition $n$ and $n + 1$ are coprime.

The result follows from LCM of Coprime Integers.