LCD Calculator
Find the least common denominator of two or more fractions. Type the fractions as a list such as 1/4, 5/6, 3/8 and the calculator returns the LCD, rewrites every fraction over it and puts them in order from least to greatest.
- Rewritten with the LCD
- 6/24, 20/24, 9/24
- Least to greatest
- 1/4 < 3/8 < 5/6
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Formula
How to use it
- Type each fraction as numerator/denominator, separated by commas.
- Read the least common denominator.
- Use the rewritten fractions to add, subtract or compare them.
Worked examples
LCD of 1/4, 5/6 and 3/8
- Least common denominator
- 24
- Rewritten with the LCD
- 6/24, 20/24, 9/24
- Least to greatest
- 1/4 < 3/8 < 5/6
LCD of 2/3 and 3/5
- Least common denominator
- 15
- Rewritten with the LCD
- 10/15, 9/15
- Least to greatest
- 3/5 < 2/3
A worked example
For 1/4, 5/6 and 3/8 the denominators are 4, 6 and 8, whose least common multiple is 24. Then 1/4 = 6/24, 5/6 = 20/24 and 3/8 = 9/24. With equal denominators the order is obvious: 1/4 < 3/8 < 5/6.
Least versus any common denominator
Multiplying all the denominators together (4 × 6 × 8 = 192) always gives a common denominator, but rarely the smallest one, and it leaves more simplifying to do at the end.
The calculator uses the denominators exactly as you type them. If a fraction is not in lowest terms, reducing it first can make the LCD smaller: 2/4 and 1/3 give 12 as typed, but 1/2 and 1/3 give 6.
Questions people ask
What is the LCD of 1/4 and 5/6?
12. The fractions become 3/12 and 10/12.
What is the LCD of 2/3 and 3/5?
15. The fractions become 10/15 and 9/15, which also shows that 2/3 is the larger one.
What is the LCD of 1/2, 1/3 and 1/4?
12. They become 6/12, 4/12 and 3/12.