jmc

Find the least common multiple of $15,20,25$ by turning the numbers into their prime factorization. $$15=3\ast 5,20=2^2\ast 5,25=5^2$$ Gather all necessary multiples $3,2^2,5^2$ when multiplied gets $300$. The multiples of $300-300,600,900,1200,1500,1800,2100$. The number of multiples between 1000 and 2000 is $\boxed{3}$.