Least common denominator calculator


What is LCD?

The lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of fractions. LCD is the smallest positive integer that has multiple denominators in the set. Fractions write with fraction bar / like 3/4.

Example: for LCD calculation of three fractions 1/2 2/3 5/4, enter 1/2 2/3 5/4.

How to calculate LCD

The same fraction we can express in many different forms. If the ratio between the numerator and denominator is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their "least common multiple".
The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.
The simple method for common computing denominators (not least at all) is to multiply all denominators.

To calculate the lowest common denominator (LCD) of two or more fractions, follow these steps:


  • Step 1: Find the denominators
    Identify the denominators of the fractions you are working with. For example:
    - For the fractions and , the denominators are 4 and 6.
  • Step 2: Find the Least Common Multiple (LCM) of the denominators
    The LCD is the least common multiple (LCM) of the denominators. To find the LCM:
    1. List the multiples of each denominator:
    - Multiples of 4: 4, 8, 12, 16, 20, ...
    - Multiples of 6: 6, 12, 18, 24, 30, ...
    2. Identify the smallest common multiple:
    - The smallest common multiple of 4 and 6 is 12.

    Alternatively, you can use the prime factorization method:
    1. Factorize each denominator into primes:
    -
    -
    2. Take the highest power of each prime factor:
    - .

  • Step 3: The LCD is the LCM
    The LCD of and is 12.

Example
Find the LCD of and :
1. Denominators: 5 and 10.
2. Multiples of 5: 5, 10, 15, 20, ...
Multiples of 10: 10, 20, 30, ...
3. The smallest common multiple is 10.
4. The LCD is 10.

Questions and word problems to LCD



more math problems »