question 10
1 part -- of 1 point

find the lcm.

(14b^{4}a^{4}, 7b^{6}a^{8}, 10b^{8}a^{4})

the lcm is

Question

question 10
1 part -- of 1 point

find the lcm.

(14b^{4}a^{4}, 7b^{6}a^{8}, 10b^{8}a^{4})

the lcm is

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Least Common Multiple", "Algebraic Monomials" ], "current_concepts": [ "Least Common Multiple", "Algebraic Monomials" ] } ## Find the LCM of the numerical coefficients $$ \begin{aligned} &\text{Coefficients: } 14, 7, 10 \ &14 = 2 \times 7 \ &7 = 7 \ &10 = 2 \times 5 \ &\text{LCM}(14, 7, 10) = 2 \times 5 \times 7 = 70 \end{aligned} $$ ## Find the LCM of the variable parts $$ \begin{aligned} &\text{Variable } a \text{ terms: } a^4, a^8, a^4 \implies \text{Highest power} = a^8 \ &\text{Variable } b \text{ terms: } b^4, b^6, b^8 \implies \text{Highest power} = b^8 \ &\text{LCM of variables} = a^8 b^8 \end{aligned} $$ ## Combine numerical and variable LCMs $$ \text{LCM} = 70a^8b^8 $$ Find the LCM. $14b^4a^4, 7b^6a^8, 10b^8a^4$ The LCM is $70a^8b^8$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Multiple" ] }

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QUESTION IMAGE

Question

Explanation:

Find the LCM of the numerical coefficients

Find the LCM of the variable parts

Combine numerical and variable LCMs

Answer: