find the least common multiple of these two expressions.

(15w^7 y^2 u^5) and (12w^3 u^4)

Question

find the least common multiple of these two expressions.

(15w^7 y^2 u^5) and (12w^3 u^4)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Least Common Multiple", "Algebraic Expressions" ], "current_concepts": [ "Least Common Multiple", "Algebraic Expressions" ] } ## Find the LCM of the numerical coefficients $$ \begin{aligned} &\text{Coefficients: } 15, 12\ &15 = 3 \times 5\ &12 = 2^2 \times 3\ &\text{LCM}(15, 12) = 2^2 \times 3 \times 5 = 60 \end{aligned} $$ ## Find the LCM of the variable parts $$ \begin{aligned} &\text{Variables: } w^7 y^2 u^5 \text{ and } w^3 u^4\ &\text{Highest power of } w: w^7\ &\text{Highest power of } y: y^2\ &\text{Highest power of } u: u^5\ &\text{LCM of variables} = w^7 y^2 u^5 \end{aligned} $$ ## Combine the numerical and variable parts $$ \text{LCM}(15w^7 y^2 u^5, 12w^3 u^4) = 60w^7 y^2 u^5 $$ $60w^7 y^2 u^5$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Multiple" ] }

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Question

Explanation:

Find the LCM of the numerical coefficients

Find the LCM of the variable parts

Combine the numerical and variable parts

Answer: