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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