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Choice C is correct. Each term in the given expression, $12x+27$, has a common factor of $3$. Therefore, the expression can be rewritten as $3\left(4x\right)+3\left(9\right)$, or $3\left(4x+9\right)$. Thus, the expression $3\left(4x+9\right)$ is equivalent to the given expression.

Choice A is incorrect. This expression is equivalent to $108x+12$, not $12x+27$.

Choice B is incorrect. This expression is equivalent to $324x+27$, not $12x+27$.

Choice D is incorrect. This expression is equivalent to $27x+72$, not $12x+27$.