Algebra Examples

$450 x^{2} y^{5}$ , $3$ , $0 x^{4} y^{3}$

Step 1

Simplify each term.

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Step 1.1

Multiply $0$ by $x^{4}$ .

$450 x^{2} y^{5}, 3, 0 y^{3}$

Step 1.2

Multiply $0$ by $y^{3}$ .

$450 x^{2} y^{5}, 3, 0$

Step 2

Since $450 x^{2} y^{5}, 3, 0$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $450, 3, 0$ then find LCM for the variable part $x^{2}, y^{5}$ .

Step 3

The LCM of $450, 3, 0$ is $0$ .

$0$

Step 4

The factors for $x^{2}$ are $x \cdot x$ , which is $x$ multiplied by each other $2$ times.

$x^{2} = x \cdot x$

$x$ occurs $2$ times.

Step 5

The factors for $y^{5}$ are $y \cdot y \cdot y \cdot y \cdot y$ , which is $y$ multiplied by each other $5$ times.

$y^{5} = y \cdot y \cdot y \cdot y \cdot y$

$y$ occurs $5$ times.

Step 6

The LCM of $x^{2}, y^{5}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

$x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot y$

Step 7

Simplify $x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot y$ .

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Step 7.1

Multiply $x$ by $x$ .

$x^{2} \cdot y \cdot y \cdot y \cdot y \cdot y$

Step 7.2

Multiply $y$ by $y$ by adding the exponents.

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Step 7.2.1

Move $y$ .

$x^{2} \cdot (y \cdot y) \cdot y \cdot y \cdot y$

Step 7.2.2

Multiply $y$ by $y$ .

$x^{2} \cdot y^{2} \cdot y \cdot y \cdot y$

Step 7.3

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 7.3.1

Move $y$ .

$x^{2} \cdot (y \cdot y^{2}) \cdot y \cdot y$

Step 7.3.2

Multiply $y$ by $y^{2}$ .

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Step 7.3.2.1

Raise $y$ to the power of $1$ .

$x^{2} \cdot (y^{1} y^{2}) \cdot y \cdot y$

Step 7.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} \cdot y^{1 + 2} \cdot y \cdot y$

Step 7.3.3

Add $1$ and $2$ .

$x^{2} \cdot y^{3} \cdot y \cdot y$

Step 7.4

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 7.4.1

Move $y$ .

$x^{2} \cdot (y \cdot y^{3}) \cdot y$

Step 7.4.2

Multiply $y$ by $y^{3}$ .

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Step 7.4.2.1

Raise $y$ to the power of $1$ .

$x^{2} \cdot (y^{1} y^{3}) \cdot y$

Step 7.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} \cdot y^{1 + 3} \cdot y$

Step 7.4.3

Add $1$ and $3$ .

$x^{2} \cdot y^{4} \cdot y$

Step 7.5

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 7.5.1

Move $y$ .

$x^{2} \cdot (y \cdot y^{4})$

Step 7.5.2

Multiply $y$ by $y^{4}$ .

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Step 7.5.2.1

Raise $y$ to the power of $1$ .

$x^{2} \cdot (y^{1} y^{4})$

Step 7.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} \cdot y^{1 + 4}$

Step 7.5.3

Add $1$ and $4$ .

$x^{2} \cdot y^{5}$

$x^{2} y^{5}$

Step 8

The LCM for $450 x^{2} y^{5}, 3, 0$ is the numeric part $0$ multiplied by the variable part.

$0 x^{2} y^{5}$