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How many positive integers N are there such that the least common multiple of N and 1000 is 1000?

  • maths -

    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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