To simplify a fraction you find the greatest common denominator (GCD) and divide both the numerator and the denominator by it.

Iterating through the smaller number is sufficient for the problem for $\mathcal{O}(\sqrt{min(N, D)})$

However a faster algorithm is using Euclid’s algorithm for GCD.

int gcd(int a, int b) {
    if (b == 0) return a;
    return gcd(b, a % b);
}

Time complexity

$\mathcal{O}(\log min(N, D))$

Problem

Read the problem.