EN

Least Common Denominator Calculator

This least common denominator calculator finds the smallest common multiple of the denominators of your fractions. Example: for 1/2, 2/3 and 3/4 the LCD is 12, and the fractions become 6/12, 8/12 and 9/12.

Source: Wikipedia – Hauptnenner. Updated: .

Separate with spaces, for example 1/2 2/3 3/4. Whole numbers and negative numerators are allowed.
My ToolboxYour inputs are saved in this browser only.

Result

Result
Least common denominator = 12; converted fractions: 6/12, 8/12, 9/12
All values
FractionMultiply byOver the LCD
1/2× 66/12
2/3× 48/12
3/4× 39/12
Sum of all fractions23/12
Sum simplified23/12
Calculation steps
  • LCD = LCM of the denominators (2, 3, 4) = 12.
  • Converting: 1/2, 2/3, 3/4 becomes 6/12, 8/12, 9/12.
  • Sum of the numerators: 6 + 8 + 9 over the denominator 12 gives 23/12, simplified 23/12.
The LCD is the smallest denominator into which all denominators divide. Each fraction is scaled by the LCD divided by its own denominator; its value does not change.

How it is calculated

The least common denominator is the least common multiple of all denominators; it puts fractions over the same denominator so you can add, subtract or compare them. The smallest possible denominator keeps the numbers manageable and makes the result easier to simplify.

How it works

First find the LCM of the denominators, for instance by prime factors or by listing multiples. Then scale each fraction by the LCD divided by its own denominator. Numerator and denominator are multiplied by the same number, so the value stays the same. Finally the numerators can be added and the result simplified. The calculator shows the factors, the converted fractions, the sum and the simplified sum.

Examples

For 1/2, 2/3 and 3/4, LCM(2, 3, 4) = 12. The factors are 6, 4 and 3, giving 6/12, 8/12 and 9/12 with the sum 23/12. For 1/6 and 1/10 the LCD is 30 rather than 60: 5/30 + 3/30 = 8/30 = 4/15. The product of the denominators also works but often gives a needlessly large denominator.

Frequently asked questions

What is the least common denominator?

The smallest denominator that all the fractions can be scaled to. It is the least common multiple of the denominators.

How do I find the LCD of 1/6 and 1/10?

The LCM of 6 and 10 is 30. Scale 1/6 by 5 and 1/10 by 3 to get 5/30 and 3/30.

Is the LCD always the product of the denominators?

No. The product is only a common denominator, often not the smallest. For 6 and 10, 60 would work, but the LCD is 30.

Sources and legal basis

As of: · Editorial policy

Related tools