# Integer Coefficients

Algebra Level 3

Find the smallest positive integer $$e$$ such that the polynomial $$ax^4 + bx^3 + cx^2 +dx + e$$ has integer coefficients and has roots at $$-2$$, $$3$$, $$5/3$$, and $$-1/2$$.

Details and assumptions

A root of a polynomial is a number $$r$$ where the polynomial is equal to 0. For example, the number $$r = 3$$ is a root of the polynomial $$2x - 6$$.

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