Algebra Examples

$\frac{7}{15 a^{2}}$ , $\frac{3}{10 a b^{3}}$ , $\frac{1}{8 b^{2}}$

Step 1

To find the LCD of a set of numbers $(\frac{7}{15 a^{2}}, \frac{3}{10 a b^{3}}, \frac{1}{8 b^{2}})$ , find the LCM of the denominators.

$LCM (15 a^{2}, 10 a b^{3}, 8 b^{2})$

Step 2

Calculate the LCM of first two denominators in the list, $15 a^{2}$ and $10 a b^{3}$ .

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Step 2.1

For each instance of a variable included in the terms, compare the power of the variable in term one with the power of the variable in term two. Return the variable with the larger exponent.

First Term: $15 a^{2}$

Second Term: $10 a b^{3}$

Step 2.2

For variable $a$ , $a^{2}$ has a greater power than $a^{1}$ , so keep $a^{2}$ .

$a^{2}$

Step 2.3

Variable: $b$

$b^{3}$

Step 2.4

Find the values of the numerical part of each term. Select the largest one, which in this case is $15$ . Multiply them together to get the current total. In this case, the current total is $150$ .

Current Total = $150$

Step 2.5

Multiply the numeric part of the denominators together.

Current Total = $15 + 15 = 30$

Step 2.6

Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.

$30$

Step 2.7

Multiply all saved numbers and variables and their powers together:

$30 a^{2} b^{3}$

Step 3

Calculate the LCM of the previously calculated LCM, $30 a^{2} b^{3}$ , and the next denominator in the list, $8 b^{2}$ . Since this is the last denominator in the list, the result is the LCD.

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Step 3.1

For each instance of a variable included in the terms, compare the power of the variable in term one with the power of the variable in term two. Return the variable with the larger exponent.

First Term: $30 a^{2} b^{3}$

Second Term: $8 b^{2}$

Step 3.2

For variable $a$ , $a^{2}$ has a greater power than $a^{0}$ , so keep $a^{2}$ .

$a^{2}$

Step 3.3

For variable $b$ , $b^{3}$ has a greater power than $b^{2}$ , so keep $b^{3}$ .

$b^{3}$

Step 3.4

Find the values of the numerical part of each term. Select the largest one, which in this case is $30$ . Multiply them together to get the current total. In this case, the current total is $240$ .

Current Total = $240$

Step 3.5

Multiply the numeric part of the denominators together.

Current Total = $30 + 30 = 60$

Step 3.6

Multiply the numeric part of the denominators together.

Current Total = $60 + 30 = 90$

Step 3.7

Multiply the numeric part of the denominators together.

Current Total = $90 + 30 = 120$

Step 3.8

$120$

Step 3.9

Multiply all saved numbers and variables and their powers together:

$120 a^{2} b^{3}$