find the lcm of $35x^3$ and $175x^7$.

the lcm is .
(simplify your answer. type your answer using exponential notation.)

Question

find the lcm of $35x^3$ and $175x^7$.

the lcm is  .
(simplify your answer. type your answer using exponential notation.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Least Common Multiple" ], "new_concepts": [ "Algebraic LCM" ], "current_concepts": [ "Least Common Multiple", "Algebraic LCM" ] } ## Find LCM of numerical coefficients $$ \begin{aligned} &35 = 5 \times 7\ &175 = 5^2 \times 7\ &\text{LCM}(35, 175) = 5^2 \times 7 = 175 \end{aligned} $$ ## Find LCM of variable parts $$ \begin{aligned} &\text{LCM}(x^3, x^7) = x^{\max(3, 7)} = x^7 \end{aligned} $$ ## Combine numerical and variable LCMs $$ \text{LCM}(35x^3, 175x^7) = 175x^7 $$ Find the LCM of $35x^3$ and $175x^7$. The LCM is $175x^7$. (Simplify your answer. Type your answer using exponential notation.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Multiple" ] }

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QUESTION IMAGE

Question

Explanation:

Find LCM of numerical coefficients

Find LCM of variable parts

Combine numerical and variable LCMs

Answer: