# 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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