Video transcriptWe're asked to rewrite the following two fractions as fractions with a least common denominator. So a least common denominator for two fractions is really just going to be the least common multiple of both of these denominators over here. And the value of doing that is then if you can make these a common denominator, then you can add the two fractions. And we'll see that in other videos. But first of all, let's just find the least common multiple. Let me write it out because sometimes LCD could meet other things. So least common denominator of these two things is going to be the same thing as the least common multiple of the two denominators over here. The least common multiple of 8 and 6. And a couple of ways to think about least common multiple-- you literally could just take the multiples of 8 and 6 and see what they're smallest common multiple is. So let's do it that way first. So multiples of six are 6, 12, 18, 24 30. And I could keep going if we don't find any common multiples out of this group here with any of the multiples in eight. And the multiples of eight are 8, 16, 24, and it looks like we're done. And we could keep going obviously-- 32, so on and so forth. But I found a common multiple and this is their smallest common multiple. They have other common multiples-- 48 and 72, and we could keep adding more and more multiple. But this is their smallest common multiple, their least common multiple. So it is 24. Another way that you could have found at least common multiple is you could have taken the prime factorization of six and you say, hey, that's 2, and 3. So the least common multiple has to have at least 1, 2, and 1, 3 in its prime factorization in order for it to be divisible by 6. And you could have said, what's the prime factorization of 8? It is 2 times 4 and 4 is 2 times 2. So in order to be divisible by 8, you have to have at least three 2's in the prime factorization. So to be divisible by 6, you have to have a 2 times a 3. And then to be divisible by 8, you have to have at least three 2's. You have to have two times itself three times I should say. Well, we have one 2 and let's throw in a couple more. So then you have another 2 and then another 2. So this part right over here makes it divisible by 8. And this part right over here makes it divisible by 6. If I take 2 times 2 times 2 times 3, that does give me 24. So our least common multiple of 8 and 6, which is also the least common denominator of these two fractions is going to be 24. So what we want to do is rewrite each of these fractions with 24 as the denominator. So I'll start with 2 over 8. And I want to write that as something over 24. Well, to get the denominator be 24, we have to multiply it by 3. 8 times 3 is 24. And so if we don't want to change the value of the fraction, we have to multiply the numerator and denominator by the same thing. So let's multiply the numerator by 3 as well. 2 times 3 is 6. So 2/8 is the exact same thing as 6/24. To see that a little bit clearer, you say, look, if I have 2/8, and if I multiply this times 3 over 3, that gives me 6/24. And this are the same fraction because 3 over 3 is really just 1. It's one whole. So 2/8 is 6/24 let's do the same thing with 5/6. So 5 over 6 is equal to something over 24. Let me do that in a different color. I'll do it in blue. Something over 24. To get the denominator from 6 to 24, we have to multiply it by 4. So if we don't want to change the value of 5/6, we have to multiply the numerator and denominator by the same thing. So let's multiply the numerator times 4. 5 times 4 is 20. 5/6 is the same thing as 20/24. So we're done. We've written 2/8 as 6/24 and we've written 5/6 as 20/24. If we wanted to add them now, we could literally just add 6/24 to 20/24. And I'll leave you there because they didn't ask us to actually do that. Show
When two or more fractions have the same denominators, they are termed as the common denominators. The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions. For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators. In this lesson, we will learn how to find the least common denominator in detail. What is Least Common Denominator?The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.  Let’s add the fractions: (2/9)+(3/4) For adding any two fractions, we first check if the denominators are the same or not as we can add or subtract only like fractions. Since the denominators are 9 and 4, we need to find a common number that is a multiple of both. This common multiple will help us simplify the problem. Thus, the least common multiple obtained for 9 and 4 is 36. Therefore, the expression can be written as: (2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36 How to Find the Least Common Denominator?In order to find the least common denominator, we can opt for either of the ways as given below:
Apart from simplifying fractions, the least common denominator can be used to arrange fractions in ascending or descending order. For example, we can arrange the following fractions in ascending order by finding their LCD: (3/5, 9/20, 4/6). Thus, the least common multiple of the denominators 5, 20, and 6 is 60. Thus, the given fractions can be written as 36/60, 27/60, 40/60. Therefore, we can conclude that 27/60 < 36/60 < 40/60. Important Notes
Topics Related to Least Common Denominator
FAQs on Least Common DenominatorWhat does Least Common Denominator Mean?The least common denominator of the given non-zero denominators is the smallest whole number that is divisible by each of the denominators. It can also be used to add fractions, subtract fractions or compare them. How Do You Find the Least Common Denominator?To find the least common denominator, one can either list the multiples of each denominator and then look for the smallest number that appears in each list or multiply both the denominators, in case the denominators have no common multiple. How to Find Least Common Denominator of Fractions?In order to find the least common denominator for a given set of fractions, simply list the multiples of each denominator then look for the smallest multiple that is common in both the lists. For example, the LCD for the two fractions, 6/7 and 2/3 will be 21 as the only least common multiple to 7, and 3 (denominators of fractions) is 21. What is the Least Common Denominator of the Exponents?The least common denominator of the exponents is the lowest common denominator that divides the denominator of the given exponent terms. Let's consider the two denominators, 3x3y2z4 and 4xy5z2
What is the Least Common Denominator of 2/3 and 5/8?In the given fractions, 2/3 and 5/8, 3 and 8 are the denominators. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, so on and the multiples of 8 are 8, 16, 24, 32, 40, so on. As we can see from the list of multiples, the smallest common multiple of 3 and 8 is 24, thus, the least common denominator of 2/3 and 5/8 is 24. Can the Least Common Denominator be Negative?No, the least common denominator cannot be negative as it represents the common multiples of the denominator. The least value of LCD can be 1 and not lesser than it which proves the point of LCD not being able to hold a negative value. Are LCD and LCM the Same?Although LCD and LCM require the same math processes, that is to find a common multiple of two or more given numbers. The key difference is that the LCD is the LCM in the denominators of the given fractions. In a way, the LCD or the least common denominators can be referred to as a special case of least common multiples. How do you find the lowest denominator of a fraction?To find the lowest common denominator, we see if the larger denominator (20) can be divided by the smaller denominator (4). We then need to work out what we need to multiply the 4 by, to make 20 (this is 5). Therefore, we multiply 1/4 by 5, so that it becomes 5/20. You can then add 5/20 and 3/20 which makes 8/20.
How do you find a common denominator?We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount. For example, consider the addition of two fractions that do not have the same denominator: Addition of 2⁄5 and 1⁄2 .
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How do you find the lowest common denominator
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