Finite Math Examples

$\frac{7}{10} - \frac{11}{18} x - \frac{1}{5} - \frac{1}{15} x$

Step 1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$10, 18, 1, 5, 15, 1$

Step 2

Since $10, 18, 1, 5, 15, 1$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $10, 18, 1, 5, 15, 1$ then find LCM for the variable part .

Step 3

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 4

$10$ has factors of $2$ and $5$ .

$2 \cdot 5$

Step 5

The prime factors for $18$ are $2 \cdot 3 \cdot 3$ .

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Step 5.1

$18$ has factors of $2$ and $9$ .

$2 \cdot 9$

Step 5.2

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

$2 \cdot 3 \cdot 3$

Step 6

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

Not prime

Step 7

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

$5$ is a prime number

Step 8

$15$ has factors of $3$ and $5$ .

$3 \cdot 5$

Step 9

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

Not prime

Step 10

The LCM of $10, 18, 1, 5, 15, 1$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 3 \cdot 3 \cdot 5$

Step 11

Multiply $2 \cdot 3 \cdot 3 \cdot 5$ .

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Step 11.1

Multiply $2$ by $3$ .

$6 \cdot 3 \cdot 5$

Step 11.2

Multiply $6$ by $3$ .

$18 \cdot 5$

Step 11.3

Multiply $18$ by $5$ .

$90$