Find the least common multiple of the expressions. $12x^5,4(x+2)$

A) $12x^5(x+2)$
B) $48x^5(x+2)$
C) $24x^6$
D) $4x^5(x+2)$
E) $3x^5(x+2)$

The least common multiple (LCM) of two algebraic expressions is the smallest expression that both original expressions can divide into. For $12x^5$ and $4(x+2)$ , the LCM must include the highest power of $x$ found in either expression, which is $x^5$ , and must also include each unique factor not common to both. Since $12x^5$ has a factor of $12$ and $x^5$ , and $4(x+2)$ has a factor of $4$ and $x+2$ , the LCM combines these unique factors without duplicating the common base of $x$ , resulting in $12x^5(x+2)$ .