To find the least common denominator (LCD) of fractions, follow these steps:
- Identify the denominators of the fractions you want to work with.
- List the multiples of each denominator. For example, if the denominators are 15 and 25:
- Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 , ...
- Multiples of 25: 25, 50, 75, 100, 125, 150 , 175, 200, ...
- Find the smallest common multiple that appears in both lists. In this example, it is 150. This number is the least common denominator.
- Rewrite each fraction as an equivalent fraction with the LCD as the denominator by multiplying numerator and denominator appropriately. For example, 215\frac{2}{15}152 becomes 20150\frac{20}{150}15020 and 125\frac{1}{25}251 becomes 6150\frac{6}{150}1506 using the LCD 150
Alternatively, you can find the LCD by:
- Finding the least common multiple (LCM) of the denominators directly, which is the same as the LCD.
- For integers and mixed numbers, convert them to improper fractions first, then find the LCM of denominators
This process ensures fractions have a common denominator for addition or subtraction, making calculations easier and more accurate
Summary:
- List multiples of each denominator.
- Identify the smallest common multiple.
- Use this number as the LCD.
- Convert fractions to equivalent fractions with the LCD.
This method works well for any set of fractions and is fundamental in fraction arithmetic
