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LCD Calculator - Least Common Denominator

Least Common Denominator (LCD)


Answer:
LCD = 24

Solution
Rewriting input as fractions if necessary:
3/2, 3/8, 5/6, 3/1

For the denominators (2, 8, 6, 1) the least common multiple (LCM) is 24.

Therefore, the least common denominator (LCD) is 24.

Rewriting the original inputs as equivalent fractions with the LCD:
36/24, 9/24, 20/24, 72/24

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Calculator Use

Use this Least Common Denominator Calculator to find the lowest common denominator (LCD) of fractions, integers and mixed numbers. Finding the LCD is important because fractions need to have the same denominator when you are doing addition or subtraction math with fractions.

What is the Least Common Denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

How to Find the LCD of Fractions, Integers and Mixed Numbers:

To find the least common denominator first convert all integers and mixed numbers (mixed fractions) into fractions. Then find the lowest common multiple (LCM) of the denominators. This number is same as the least common denominator (LCD).You can then write each term as an equivalent fraction with the same LCD denominator.

Steps to find the LCD of fractions, integers and mixed numbers

  1. Convert integers and mixed numbers to improper fractions
  2. Find the LCD of all the fractions
  3. Rewrite fractions as equivalent fractions using the LCD

Example Using the Lowest Common Denominator Calculator

Find the LCD of: 1 1/2, 3/8, 5/6, 3

  • Convert integers and mixed numbers to improper fractions.
    3/8 and 5/6 are already fractions so we can use those as they are written.
    1 1/2 is the same as (1/1) + (1/2). Using the formula for adding fractions, ((n1*d2)+(n2*d1)) / (d1*d2), we get ((1*2)+(1*1)) / (1*2) = 3/2.
    3 can be rewritten as a fraction as 3/1
  • Equivalent fractions are: 3/2, 3/8, 5/6, 3/1
  • Now find the least common denominator (LCD) (or the least common multiple (LCM) of the denominators)
    • LCD = 24
  • Rewriting the fractions as equivalent fractions using the LCD
    • 36/24, 9/24, 20/24, 72/24

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Cite this content, page or calculator as:

Furey, Edward "LCD Calculator - Least Common Denominator"; from https://www.calculatorsoup.com - Online Calculator Resource.

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