Least number one short of every divisor from 2 to 10

Find the smallest positive integer that leaves remainder $n$ on division by $n+1$, for every $n$ from $1$ to $9$ (so remainder $1$ mod $2$, remainder $2$ mod $3$, up to remainder $9$ mod $10$).

$2519$. Each condition says $X\equiv -1 \pmod{n+1}$, so $X+1$ is divisible by all of $2,\dots,10$. The least such $X+1$ is $\operatorname{lcm}(2,\dots,10)=2520$, giving $X=2519$.