We know that $\lcm(1,\dots,n)$ is approximately $e^n$ and and also we know that $\gcd(2^a-1, 2^b-1)=2^{\gcd(a,b)}-1$.

I wonder if there exists an upperbound/lowerbound/approximation for $\lcm(2^1-1, 2^2-1,\dots,2^n-1)$.