Numbers and Quantities
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To use this method, you need to be comfortable with prime number factorization. This method works no matter what your denominators are.
Rule
Lowest Common Denominator, LCD
- 1.
- Write down all the denominators below each other.
- 2.
- Find the prime factors of each denominator.
- 3.
- All the factors of the different denominators have to be included as the factors of the common denominator.
- 4.
- The product of those factors is your lowest common denominator.
Example 1
Find .
First, you find the common denominator:
| Denominator | Factors |
| LCD | |
The least common denominator is then:
Then, you expand the fractions so all of them have the common denominator: is missing the factors and ; is missing the factors , and ; and is missing the factors , and to have all the factors in the LCD. That gives you
