Least common multiple in binomial expansion If I sum the terms of a binomial expansion, which would be the least common multiple of all the denominators?
Say
$\displaystyle \binom{n}{0} + \binom{n}{1} + \binom{n}{2} + \ldots + \binom{n}{n}$
$1 \displaystyle + \frac{n!}{(n - 1)!} + \frac{n!}{2!(n - 2)!} + \ldots + 1$
$n$ may be odd or even (if $n$ is even, when $k = n/2$ we have a $(n - n/2)^2$ denominator). 
I modify the original post in order to better understand my question. "What is $\operatorname{lcm} \{ k!(n - k)! \}$ for $k = 0, \ldots, n$"?
Do you have any hints?
Thank you anyway!

In every case the fraction reduced to lowest terms has denominator $1$, and $\operatorname{lcm}(1,1,1,\ldots,1)=1$.
