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.

## Answer this Question

## Related Questions

- maths - How many positive integers N are there such that the least common ...
- Maths - The number 1000 can be written in several ways as a sum of one or more ...
- maths - If the product of two positive integers is 363, and the least common ...
- maths - If the product of two positive integers is 363, and the least common ...
- Maths Please Help - Suppose a,b, and c are positive integers such that a+b+c+ab+...
- MATHS~~ - How many positive integers less than or equal to 1000 are common ...
- inTEGERS! - How many positive integers less than 1000 are odd but not a multiple...
- Maths - Find the number of positive integers <1000 that can be expressed as 2...
- maths - Find the number of positive integers <1000 that can be expressed as 2...
- MATHS!!!! - For how many odd positive integers n<1000 does the number of ...