Pre-Algebra Examples

$\frac{9}{10}$ , $\frac{5}{8}$

Step 1

To find the LCM for a list of fractions such as $LCM (\frac{a}{b}, \frac{c}{d})$ using GCF:

1. Find the LCM of $a$ and $c$ .

2. Find the GCF of $b$ and $d$ .

3. $LCM (\frac{a}{b}, \frac{c}{d}) = \frac{LCM (a, c)}{GCF (b, d)}$ .

Step 2

Calculate the LCM of the numerators $9, 5$ .

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Step 2.1

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 2.2

$9$ has factors of $3$ and $3$ .

$3 \cdot 3$

Step 2.3

Since $5$ has no factors besides $1$ and $5$ .

$5$ is a prime number

Step 2.4

The LCM of $9, 5$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$3 \cdot 3 \cdot 5$

Step 2.5

Multiply $3 \cdot 3 \cdot 5$ .

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Step 2.5.1

Multiply $3$ by $3$ .

$9 \cdot 5$

Step 2.5.2

Multiply $9$ by $5$ .

$45$

Step 3

Factor out the GCF of $2$ from $10 + 8$ .

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Step 3.1

Factor out the GCF of $2$ from each term in the polynomial.

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Step 3.1.1

Factor out the GCF of $2$ from the expression $10$ .

$2 (5) + 8$

Step 3.1.2

Factor out the GCF of $2$ from the expression $8$ .

$2 (5) + 2 (4)$

Step 3.2

Since all the terms share a common factor of $2$ , it can be factored out of each term.

$2 (5 + 4)$

Step 4

Divide

$\frac{45}{2}$