Smallest number one short of a multiple of 2 to 10

What is the least positive integer $N$ such that, for each $k=2,3,\dots,10$, dividing $N$ by $k$ leaves remainder $k-1$?

$2519$. The condition says $N+1$ is divisible by every $k$ from $2$ to $10$, so $N+1$ is a multiple of $\operatorname{lcm}(2,\dots,10)=2520$. The smallest choice is $N=2519$.