1. **State the problem:** Find the Least Common Multiple (LCM) of the algebraic expressions $(3x + 9)(4x + 4)$ and $7x + 7$. 2. **Rewrite expressions in factored form:** - First expression: $(3x + 9)(4x + 4)$ can be factored as $3(x + 3) \times 4(x + 1)$ which is $12(x + 3)(x + 1)$. - Second expression: $7x + 7$ can be factored as $7(x + 1)$. 3. **Identify common and unique factors:** - Common factor: $(x + 1)$ - Unique factors: $12$, $(x + 3)$, and $7$ 4. **LCM rule:** The LCM of algebraic expressions is the product of the highest powers of all factors appearing in any expression. 5. **Construct the LCM:** - Take the highest coefficient factor: LCM of $12$ and $7$ is $84$ (since $12 = 2^2 \times 3$, $7$ is prime, so $84 = 2^2 \times 3 \times 7$). - Include all unique factors: $(x + 3)$ and $(x + 1)$. 6. **Final LCM:** $$\text{LCM} = 84(x + 3)(x + 1)$$ This is the least common multiple without expanding or simplifying further.