Welcome to the LCD calculator - an intuitive tool that helps you find the least common denominator. All you need to do is input up to five fractions and we'll calculate the LCD and equivalent fractions with that denominator. Pretty straightforward, huh? 😉 Show However, if you'd like to first learn what the least common denominator is or how to find the least common denominator by hand ✍️ - we're here for you too. Scroll down and read our short & informative article about the lowest common denominator!
The least common denominator, also known as the lowest common denominator, is the lowest common multiple of the denominators of a given set. Struggling to differentiate between LCD and LCM? Check our LCM calculator first. Usually, we search for the least common denominator when we want to perform an operation on fractions, like adding fractions (and subtracting) or comparing fractions. For example:
However, if you've just googled the question "What is a LCD?", and you looked for the least common denominator definition, the search results may be a bit surprising to you 😮. The abbreviation LCD also stands for a Liquid Crystal Display - a type of display we have in our computers 💻, TV screens 📺, digital cameras 📽️, watches ⌚ and smartphones 📱. So next time, try "What is a LCD in math?" instead 😉
Well, the easiest and most straightforward method is to use our LCD calculator - that's why you are here, right? 😉 Jokes aside - we really appreciate that you'd like to learn how to find the least common denominator. There are a couple of methods, and we'll describe four of them here. So let's present them with a relatively simple example: Assume that we have three fractions: 1/2, 3/8, and 11/12. What's the LCD value? What are the equivalent fractions, with the same denominator? First, we need to find the lowest common denominator of our fractions. Read about the four methods below and choose the way you like the most.
Listing multiples is a brute force method. It may be useful in special cases, e.g., if the numbers are relatively small. So, how to find the least common denominator? Make a list of the multiples of each number, until you find the first common multiple of all the numbers:
It's usually not a recommended method. Imagine listing the common denominators of 2 and 1000 - it doesn't make much sense, does it? :)
Another method to find out the lowest common denominator is the prime factorization (which you can read more about on our prime factorization calculator 😉) method:
You can calculate the LCD from the Greatest Common Factor (GCF) (as in our GCF calculator) value: LCD(a,b) = |a * b| / GCF(a,b) where |a * b| is the absolute value of a * b.
The last method is the ladder method. Many students like this technique, so check it out, and maybe you'll have a new favorite:
Write that prime number on the left-hand side:
2 2 8 12
Now that you know the LCD value, you can come to the second step - finding the fractions that are equivalent to your basic fractions, but with the same denominator - 24 in our case:
And that's it! After the reading, you've (hopefully) understood what the least common denominator is and learned about four methods that can help you find the LCM in math. So, what now? It's time to check how the LCD calculator works!
Check out this step-by-step guide if you have any doubts on how to use our tool:
Additionally, the tool displays the equivalent fractions with the LCD value as the denominator:
Now that you know what the least common denominator is - and how to find it - let's talk about some LCD applications. We can almost hear you moaning "But where will I ever use it?" No worries - the lowest common denominator is helpful in many life situations. You can use it any time you want to "align" two or more things of different lengths, e.g.:
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 8 and 9 is 72. LCM(8,9) = 72 Least Common Multiple of 8 and 9 with GCF FormulaThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b). GCF(8,9) = 1 LCM(8,9) = ( 8 × 9) / 1 LCM(8,9) = 72 / 1 LCM(8,9) = 72 Least Common Multiple (LCM) of 8 and 9 with PrimesLeast common multiple can be found by multiplying the highest exponent prime factors of 8 and 9. First we will calculate the prime factors of 8 and 9. Prime Factorization of 8
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is: 8 = 23 Prime Factorization of 9
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is: 9 = 32 Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 9. LCM(8,9) = 23 × 32 |