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.

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