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
- 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 Mira
Centipede Miroslava 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. - Three-day trip
George went on a moped for a three-day trip. He drove 90 km on the first day, 30 km on the second day, and 60 km on the third day. He always drove at the same average speed and always the whole number of hours. Calculate the average speed if George drove - LCD two fractions
What is the least common denominator of 11/15 and 12/19? - Grand Pardubice Steeplechase
Jirka decided to divide the winnings from the bet in Grand Pardubice Steeplechase (Velká Pardubická) between himself and his three younger brothers according to age in the ratio of 2:3:5:7. They paid each amount in whole crowns. One of the amounts was CZK
- Multiple 83863
The least common multiple of 2190 and b is 13140. What is b? - Determine 6
Determine the least common denominator 3/4 and -5/6 - A person 3
A person distributes his pens among four friends A, B, C and D in the ratio 1/3 : 1/4 : 1/5 : 1/6. What is the minimum number of pens that the person should have? - Treasury 73334
Peter has only two crowns in the treasury and can divide them both in a ratio of 4:5 and in a ratio of 4:7. How many crowns does Peter have in the money box if the amount saved is less than 300 CZK? - Meadow
On the meadow, there are horses, cows, and sheep grazing together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equal. How many horses, cows, and sheep are in the mead - Ratio
Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order. - Compare three fractions
Which of the three rational numbers is the largest? 1/7, 6/17, 4/17 - Reminder and quotient
Numbers A = 135 and B = 315 are given. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1.
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