Posted by chirag on Tuesday, February 12, 2013 at 9:22am.
How many positive integers N are there such that the least common multiple of N and 1000 is 1000?

maths  Steve, Tuesday, February 12, 2013 at 10:26am
LCM(1000,n) = 1000n/GCD(1000,n)
so
1000GCD(1000,n) = 1000n
GCD(1000,n) = n
So, all factors of 1000 fit the bill. You can easily figure that out.