What is the name and what are the properties of the smallest integer divisible by all integers $1\ldots n$?
Clearly, $n!$ would do the trick, but it is generally not the smallest such number.
So far, I only came up with a recursive definition, i.e.
$f(n)=\frac{n\,f(n-1)}{\mathrm{gcd}(n,f(n-1)}$ starting with $f(1)=1$.
This nicely gives e.g. the first 12 such numbers: 1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520, 27720, 27720.
Someone must have come across this before... Thanks.
