AHSME 1951 Problem 37

A number which when divided by $10$ leaves a remainder of $9$, when divided by $9$ leaves a remainder of $8$, by $8$ leaves a remainder of $7$, etc., down to where, when divided by $2$, it leaves a remainder of $1$, is: $\textbf{(A)}\ 59 \textbf{(B)}\ 419 \textbf{(C)}\ 1259 \textbf{(D)}\ 2519 \textbf{(E)}\ \text{none of these answers}$