## Least Common Denominator

### Least Common Denominator: Learn

When working with more than one fraction, it is often helpful to find a common denominator. The easiest and most useful to work with is known as the least common denominator or LCD.

To find the LCD, all you need to do is find the least common multiple (LCM) of the two denominators. Please visit the LCM lesson if you need more practice finding least common multiples.

Example: For the fractions 2/9 and 3/12, the LCD is 36, because 36 is the LCM of the two denominators.

However, the LCD itself is not very useful. We need to rewrite the fractions using the LCD as a new denominator.

How to rename fractions and use the Least Common Denominator:

• Divide the LCD by one denominator.
• Multiply the numerator times this quotient.
• Repeat the process for the other fraction(s)

Example: Rewrite 2/9 and 3/12 using their LCD
We have already identified the LCD as 36

• For the first fraction (2/9), the denominator is nine, so we need the result of 36/9 = 4 as a new multiplier. Then the numerator, 2, times this new multiplier, 4, equals 8. So our re-written fraction is 8/36.
• For the second fraction (3/12), the denominator is twelve, so we need the result of 36/12 = 3 as a new multiplier. Then the numerator, 3, times this new multiplier, 3, equals 9. So our re-written fratcion is 9/36.

Alternatively, some like to write it out in a similar format to what they use when simplifying fractions:

2 * 4
9 * 4
=
8
36
and
3 * 3
12 * 3
=
9
36

This helps you remember that we are not actually changing the value of the fraction. By multiplying the same number over itself, we are really multiplying by 1, and that does not change the value of the number.

### LCD: Practice

#### Rename the fractions using their least common denominator

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