I was thinking the other day about the following function - a sort of prime factorial: $$f(n) = \text{lcm}(1,2,\cdots,n) $$
Does this function have a name? Does it have any interesting properties analagous to $n!$ (e.g. a version of Sterling's formula?)
EDIT A previous version of this question asserted that $f(n)$ is equal to the primorial. As pointed out below, that is demonstrably false.
The function $\text{lcm}(1, \dots, n)$ is equal to $$e^{\psi(n)}$$
where $\psi$ is the second Chebyshev function. Many proofs of the Prime Number Theorem proceed by first estimating the Chebyshev function, so you'll find a wealth of information on the Wikipedia page. To make a long story short, the least common multiple of the integers from $1$ to $n$ is approximately $e^n$.