2019 AIME II Problems/Problem 3

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Find the number of $7$-tuples of positive integers $(a,b,c,d,e,f,g)$ that satisfy the following systems of equations: $\begin{align*} abc&=70,\\ cde&=71,\\ efg&=72. \end{align*}$ (Error compiling LaTeX. ! Package amsmath Error: \begin{align*} allowed only in paragraph mode.)

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