Questions: Find the least common multiple of these two expressions. 12x^5y^7u^2 and 15x^8u^3

Transcript text: Find the least common multiple of these two expressions. $12 x^{5} y^{7} u^{2}$ and $15 x^{8} u^{3}$

Solution

Solution Steps

Step 1: Define the Expressions

We start with the two expressions:
$ expr1 = 12 u^{2} x^{5} y^{7} $
$ expr2 = 15 u^{3} x^{8} $

Step 2: Find the LCM of the Coefficients

Next, we calculate the least common multiple (LCM) of the coefficients $ 12 $ and $ 15 $:
\[ \text{coeff\_lcm} = \text{lcm}(12, 15) = 60 \]

Step 3: Determine the LCM of the Variables

We then find the highest power of each variable present in both expressions:

For $ x $: $ \max(5, 8) = 8 $
For $ y $: $ \max(7, 0) = 7 $
For $ u $: $ \max(2, 3) = 3 $

Step 4: Combine the Results

Finally, we combine the LCM of the coefficients with the highest powers of the variables to obtain the least common multiple of the two expressions:
\[ \text{lcm\_expr} = 60 u^{3} x^{8} y^{7} \]

Final Answer

$\boxed{60 x^{8} y^{7} u^{3}}$

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