Question

find the least common multiple of these two expressions.

(12u^5 x^6 v^8) and (20u^4 x^7)

Explanation:

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<reasoning>

Find the LCM of the numerical coefficients

\[

$$\begin{aligned} &\text{lcm}(12, 20) = 60 \end{aligned}$$

\]

Find the highest power of each variable

\[

$$\begin{aligned} &u: \max(5, 4) = 5 \\ &x: \max(6, 7) = 7 \\ &v: \max(8, 0) = 8 \end{aligned}$$

\]

Combine the numerical LCM and variable powers

\[
\text{LCM} = 60u^5x^7v^8
\]
</reasoning>

<answer>
Find the least common multiple of these two expressions.
\(12u^5x^6v^8\) and \(20u^4x^7\)
<blank>\(60u^5x^7v^8\)</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Least Common Multiple"
]
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</post_analysis>

Answer:

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"step_cot",
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</pre_analysis>

<reasoning>

Find the LCM of the numerical coefficients

\[

$$\begin{aligned} &\text{lcm}(12, 20) = 60 \end{aligned}$$

\]

Find the highest power of each variable

\[

$$\begin{aligned} &u: \max(5, 4) = 5 \\ &x: \max(6, 7) = 7 \\ &v: \max(8, 0) = 8 \end{aligned}$$

\]

Combine the numerical LCM and variable powers

\[
\text{LCM} = 60u^5x^7v^8
\]
</reasoning>

<answer>
Find the least common multiple of these two expressions.
\(12u^5x^6v^8\) and \(20u^4x^7\)
<blank>\(60u^5x^7v^8\)</blank>
</answer>

<post_analysis>
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"Mathematics",
"Algebra",
"Least Common Multiple"
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