The Least Common Denominator (LCD) is the Least Common Multiple of two or more
How to find the Least Common Denominator:
- Find the Greatest Common Factor of the denominators.
- Multiply the denominators together.
- Divide the product of the denominators by the Greatest Common Factor.
Example: Find the LCD of 2/9 and 3/12
- Determine the Greatest Common Factor of 9 and 12 which is 3
- Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)
- OR - Divide one of the denominators by the GCF and multiply the quotient times the other
denominator (9/3=3, 3*12=36)
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: Add 2/9 + 3/12
- LCD is 36
- First fraction (2/9): 36/9 = 4, 4*2 = 8, first fraction is renamed as 8/36
- Second fraction (3/12): 36/12 = 3, 3*3 = 9, second fraction is renamed as 9/36
- It is possible to add or subtract fractions that have the same denominator
- 8/36 + 9/36 = 17/36