jmc

A number with 15, 20 and 25 as factors must be divisible by their least common multiple (LCM). Because $15=3\times 5$, $20=2^2\times 5$, and $25=5^2$, the LCM of 15, 20 and 25 is $2^2\times 3\times 5^2=300$. There are $\boxed{3}$ multiples of 300 between 1000 and 2000: 1200, 1500 and 1800.