posted by chirag .
How many positive integers N are there such that the least common multiple of N and 1000 is 1000?
LCM(1000,n) = 1000n/GCD(1000,n)
1000GCD(1000,n) = 1000n
GCD(1000,n) = n
So, all factors of 1000 fit the bill. You can easily figure that out.