QuestionFind the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the least common multiple (LCM) of two expressions. . The two expressions are $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{}$

STEP 2

The least common multiple (LCM) of two expressions is the smallest expression that is a multiple of both expressions. To find the LCM, we need to take the highest power of each variable from both expressions.

STEP 3

Let's first find the LCM of the coefficients (the numerical parts) of the two expressions. The coefficients are16 and6. We can find the LCM of these numbers by listing their multiples and finding the smallest number that appears in both lists.

STEP 4

The multiples of16 are16,32,48,64,80,96,112,128,144,160,176,192,208,224,240, ...
The multiples of6 are6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,210,216,222,228,234,240, ...
The smallest number that appears in both lists is48. So, the LCM of16 and6 is48.

STEP 5

Next, let's find the LCM of the variable $u$ . The powers of $u$ in the two expressions are3 and7. The LCM of $u$ is $u$ raised to the highest power, which is7. So, the LCM of $u^{3}$ and $u^{7}$ is $u^{7}$ .

STEP 6

Then, let's find the LCM of the variable $v$ . The power of $v$ in the first expression is0 (since $v$ does not appear in the first expression, we can consider its power to be0) and the power of $v$ in the second expression is5. The LCM of $v$ is $v$ raised to the highest power, which is5. So, the LCM of $v^{0}$ and $v^{5}$ is $v^{5}$ .

STEP 7

Finally, let's find the LCM of the variable $x$ . The powers of $x$ in the two expressions are4 and2. The LCM of $x$ is $x$ raised to the highest power, which is4. So, the LCM of $x^{4}$ and $x^{2}$ is $x^{4}$ .

STEP 8

Now, we can write the LCM of the two expressions by multiplying together the LCMs of the coefficients and the variables. $LCM =48 \cdot u^{7} \cdot v^{5} \cdot x^{4}$ So, the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ is $48 u^{7} v^{5} x^{4}$ .

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QuestionFind the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to find the least common multiple (LCM) of two expressions. . The two expressions are $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{}$

STEP 2

The least common multiple (LCM) of two expressions is the smallest expression that is a multiple of both expressions. To find the LCM, we need to take the highest power of each variable from both expressions.

STEP 3

Let's first find the LCM of the coefficients (the numerical parts) of the two expressions. The coefficients are16 and6. We can find the LCM of these numbers by listing their multiples and finding the smallest number that appears in both lists.

STEP 4

STEP 5

Next, let's find the LCM of the variable $u$ . The powers of $u$ in the two expressions are3 and7. The LCM of $u$ is $u$ raised to the highest power, which is7. So, the LCM of $u^{3}$ and $u^{7}$ is $u^{7}$ .

STEP 6

STEP 7

Finally, let's find the LCM of the variable $x$ . The powers of $x$ in the two expressions are4 and2. The LCM of $x$ is $x$ raised to the highest power, which is4. So, the LCM of $x^{4}$ and $x^{2}$ is $x^{4}$ .

STEP 8

Now, we can write the LCM of the two expressions by multiplying together the LCMs of the coefficients and the variables. $LCM =48 \cdot u^{7} \cdot v^{5} \cdot x^{4}$ So, the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ is $48 u^{7} v^{5} x^{4}$ .

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QuestionFind the least common multiple of 16u3x416 u^{3} x^{4}16u3x4 and 6u7v5x26 u^{7} v^{5} x^{2}6u7v5x2.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the least common multiple (LCM) of two expressions. . The two expressions are 16u3x416 u^{3} x^{4}16u3x4 and 6u7v5x6 u^{7} v^{5} x^{}6u7v5x

STEP 2

The least common multiple (LCM) of two expressions is the smallest expression that is a multiple of both expressions. To find the LCM, we need to take the highest power of each variable from both expressions.

STEP 3

Let's first find the LCM of the coefficients (the numerical parts) of the two expressions. The coefficients are16 and6. We can find the LCM of these numbers by listing their multiples and finding the smallest number that appears in both lists.

STEP 4

STEP 5

Next, let's find the LCM of the variable uuu. The powers of uuu in the two expressions are3 and7. The LCM of uuu is uuu raised to the highest power, which is7. So, the LCM of u3u^{3}u3 and u7u^{7}u7 is u7u^{7}u7.

STEP 6

STEP 7

Finally, let's find the LCM of the variable xxx. The powers of xxx in the two expressions are4 and2. The LCM of xxx is xxx raised to the highest power, which is4. So, the LCM of x4x^{4}x4 and x2x^{2}x2 is x4x^{4}x4.

STEP 8

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QuestionFind the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ .

Assumptions1. We are asked to find the least common multiple (LCM) of two expressions. . The two expressions are $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{}$

Next, let's find the LCM of the variable $u$ . The powers of $u$ in the two expressions are3 and7. The LCM of $u$ is $u$ raised to the highest power, which is7. So, the LCM of $u^{3}$ and $u^{7}$ is $u^{7}$ .

Finally, let's find the LCM of the variable $x$ . The powers of $x$ in the two expressions are4 and2. The LCM of $x$ is $x$ raised to the highest power, which is4. So, the LCM of $x^{4}$ and $x^{2}$ is $x^{4}$ .