2003 AMC 8 Problem 19

How many integers between 1000 and 2000 have all three of the numbers 15, 20, and 25 as factors?

\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.