Question: Suppose that 1 2 3 x ^ 2 4 7 x + c = 0 for some integer constant c , has a rational root

Suppose that
123x^247x+c=0
for some integer constant c, has a rational root of the form x=ab (assume that the fraction ab is completely reduced, i.e., a and b have no common factors). What is the maximum possible value of b?

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