Least common denominator calculator
LCD(1/2, 2/3, 5/4) = LCM(2, 3, 4) = 22×3 = 12
1/2 = 6/12
2/3 = 8/12
5/4 = 15/12
*** For example, to continue with the fraction calculator, calculate the sum of fractions 1/2 + 2/3 + 5/4.
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
- LCD 2
The least common denominator of 2/5, 1/2, and 3/4 - Fractions
Sort fractions z1 = (20)/(9); z2 = (10)/(21); z3 = (15)/(14) by their size. The result writes as three serial numbers 1,2,3. - Preparatory test
Less than 50 pupils go to 9A class. A third of the pupils wrote the preparatory test with a one, a quarter with a two, no one wrote with a three, and nine pupils with a four. How many students from 9A wrote the test with a five? - Centipede 4257
Centipede Mirka consists of a head and several articles. Each pair has one pair of legs. When it got cold, she decided to get dressed. Therefore, she put a sock on her left foot from the end of the third article and then in every other third article. Simi
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCMmore math problems »
