You must add $\frac{4}{x^2-5x+6}+\frac{1}{2x}$. A student uses the LCD $2x(x-2)(x-3)$. Provide the best justification statement for why this LCD is appropriate.

Because multiplying denominators gives an LCD and $2x(x-2)(x-3)$ is one such product

Because the LCD must always include an $x$ term, a $2$, and both binomials regardless of factors

Because $x^2-5x+6$ factors to $(x-2)(x-3)$, and $2x$ supplies both the numeric factor $2$ and the factor $x$ from the second denominator

Because the LCD should be $x(x-2)(x-3)$ without the $2$, since coefficients never affect the LCD