Troll G.C.D!

For an integer \(30 \le k \le 70\), let \(M\) be the maximum possible value of \[ \dfrac{A}{\gcd(A,B)} \quad \text{where } A = \dbinom{100}{k} \text{ and } B = \dbinom{100}{k+3}. \] Find \(M\) \(\text{mod}\) \(1000\)

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