Minimum Digit Sum Fraction

Algebra Level 3

Let $$S(N)$$ denote the digit sum of the integer $$N$$. As $$N$$ ranges over all 3-digit positive numbers, what value of $$N$$ would give the minimum of $$M = \frac{N}{S(N)}$$?

Details and assumptions

The number $$12=012$$ is a 2-digit number, not a 3-digit number.

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is $$1 + 1 + 2 + 3 = 7$$.

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