Pre-Algebra Examples

$29^{4}$ , $x^{2}$

Step 1

Since $707281, x^{2}$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $707281, 1$ then find LCM for the variable part $x^{2}$ .

Step 2

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 3

The prime factors for $707281$ are $29 \cdot 29 \cdot 29 \cdot 29$ .

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Step 3.1

$707281$ has factors of $29$ and $24389$ .

$29 \cdot 24389$

Step 3.2

$24389$ has factors of $29$ and $841$ .

$29 \cdot 29 \cdot 841$

Step 3.3

$841$ has factors of $29$ and $29$ .

$29 \cdot 29 \cdot 29 \cdot 29$

Step 4

The number $1$ is not a prime number because it only has one positive factor, which is itself.

Not prime

Step 5

The LCM of $707281, 1$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$29 \cdot 29 \cdot 29 \cdot 29$

Step 6

Multiply $29 \cdot 29 \cdot 29 \cdot 29$ .

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Step 6.1

Multiply $29$ by $29$ .

$841 \cdot 29 \cdot 29$

Step 6.2

Multiply $841$ by $29$ .

$24389 \cdot 29$

Step 6.3

Multiply $24389$ by $29$ .

$707281$

Step 7

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 8

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

$x \cdot x$

Step 9

Multiply $x$ by $x$ .

$x^{2}$

Step 10

The LCM for $707281, x^{2}$ is the numeric part $707281$ multiplied by the variable part.

$707281 x^{2}$