Calculator UseUse this Least Common Denominator Calculator to find the lowest common denominator (LCD) of fractions, integers and mixed numbers. Finding the LCD is important because fractions need to have the same denominator when you are doing addition or subtraction math with fractions. Show
What is the Least Common Denominator?The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator. How to Find the LCD of Fractions, Integers and Mixed Numbers:To find the least common denominator first convert all integers and mixed numbers (mixed fractions) into fractions. Then find the lowest common multiple (LCM) of the denominators. This number is same as the least common denominator (LCD).You can then write each term as an equivalent fraction with the same LCD denominator. Steps to find the LCD of fractions, integers and mixed numbers
Example Using the Lowest Common Denominator CalculatorFind the LCD of: 1 1/2, 3/8, 5/6, 3
Related CalculatorsWe also have calculators for least common multiple, math with fractions, simplifying fractions, math with mixed numbers, and comparing fractions. LCM of two numbers is the smallest common multiple or a positive integer which is divisible completely by both the numbers. LCM is the least common multiple between two or more numbers which is wholly divisible by them. Suppose the LCM of a and b is equal to c, then c should be evenly divisible by both a and b. To find LCM of more than two numbers read here. We will also learn to find the LCM of fractions using the formula and with the help of examples. Table of contents:
What is LCM of 2 Numbers?The LCM of Least Common Multiple of 2 numbers is the smallest number, divisible by the two numbers, evenly. It is also known as the Least Common Divisor or LCD. For example, consider 2 numbers as 10 and 4. Now, the smallest number that can be divided by 10 and 4 evenly, will be 20. We can also find the LCM using prime factorisation method. How to Find LCM of Two Numbers?There are 4 main methods to calculate the least common multiple of 2 numbers. These methods are:
Listing Multiples or Brute Force Method of Finding LCMIn this method, the multiples of each number are listed until the first common multiple is found. Consider the example of 4 and 10. For this method, the multiples of 4 and 10 are to be listed. Multiples of 4: 4, 8, 12, 16, 20, 24, 28 Multiples of 10: 10, 20, 30, 40 Here, the number 20 is the first common multiple of both 4 and 10. So, the LCM of 4, 10 is 20. Prime Factorization Method of Finding LCMThe prime factorization is one of the most common ways of finding LCM. To find the LCM of two numbers 30 and 45, the steps are as follows: Step 1: To first list the prime factors of each number. 30 = 2 × 3 × 5 Step 2: Next multiply each factor the maximum number of times it occurs in either number. If the same factor occurs more than once in both numbers, then multiply the factor the maximum number of times it occurs. The occurrence of Numbers in the above example: 2: one time After calculating the LCM, always check
to be sure your answer can be divided evenly by both numbers. Division Method or Ladder Method of Finding LCMIn this method, the two numbers are simultaneously divided with prime numbers until the division is even. When there are no more primes that evenly divide into both numbers, multiply the divisors to get the LCM. For example, consider 4 and 10 as two Division Method or Ladder Method of Finding LCM Here, the LCM of 24, 15 will be 2×2×2×3×5=23×3×5=120 GCD or GCF Method of Finding LCMThis method is used only when the greatest common factor of two numbers is given. The formula used to find the LCM using the GCF or GCD is: L.C.M. = a×b/ gcd(a,b) For example, for 15 and 24, the GCF will be 3. So, the LCM will be (15 × 24) / 3 = 3. Solved ExamplesExample 1: Find the L.C.M of 18 and 24 by using the division method? Solution:
For numbers 18 and 24 = 2 × 2 × 2 × 3 × 3 = 72 is the LCM. Example 2: Find the Least Common Multiples of these sets of numbers: 3, 9, 21. Solution: Step 1: List the prime factors of each. Step 2: Multiply each factor the maximum number of times it occurs in any of the numbers. The occurrence of Numbers in the above example: 3: two times 7: one time 3 x 3 x 7 = 63 9 has two 3s, and 21 has one 7, so we multiply 3 two times, and 7 once. This gives us 63, the lowest number that can be divided evenly by 3, 9, and 21. Example 3: Find the Least common factor of 12, 80. Solution: Step 1: List the prime factors of each. Step 2: Step 3: The occurrence of Numbers in the above example: 2: 4 times 3: 1 time 5: 1 time 2 x 2 x 2 x 2 x 3 x 5 =240 12 has one 3, and 80 has four 2’s and one 5, so we multiply 2 four times, 3 once, and five once. This gives us 240, the lowest number that can be divided by both 12 and 80. How to Find LCM of Fractions?LCM of two fractions will be the smallest common multiple which can be divided by the two fractions, wholly. Formula to find the LCM of two fractions is: \(\begin{array}{l}L.C.M = \frac{LCM\, of\, the\, Numerators}{HCF\, of\, the\, Denominators}\end{array} \) Suppose a/b and c/d are two fractions. Then to find the LCM of a/b and c/d follow the below steps: Step 1: Find LCM of the numerator i.e. LCM (a,c) Step 2: Find HCF of denominator i.e. HCF (b,d) Step 3: Put the values in the given formula This is the shortcut method to find the LCM of fractions. Let us understand with the help of an example. Example: LCM of ⅘ and 3/7 As per the formula, LCM of any two fractions can be found: L.C.M = LCM of the numerators/HCF of denominators Now first we need to find the LCM of numerators. Here the numerators are 4 and 3. Therefore LCM (4,3) = 12 Second step is to find HCF of denominators. Hence, HCF of 5 and 7 is: 5 = 1 x 5 7 = 1 x 7 HCF (5,7) = 1 Third step will be the last step to put the values of LCM(4,3) and HCF(5,7) in the formula; Therefore, LCM (⅘ and 3/7) = 12/1 = 12 Recheck: If 12 is the LCM of ⅘ and 3/7, we should check if 12 is wholly divided by ⅘ and 3/7. Hence, 12/(⅘) = (12 x 5)/4 = 3 x 5 = 15 12/(3/7) = (12 x 7)/3 = 4 x 7 = 28 Hence, 12 is the right answer. Register to BYJU’S to understand more mathematical topics with a detailed explanation and more practice examples. Frequently Asked Questions – FAQsLCM of any two numbers is the smallest common multiple or smallest common integer which is divisible by both the numbers completely. If LCM of a and b is c, then c should be
divisible by a and b both. To find the LCM of 2 and 4, let us write the multiples of both the numbers first. To find LCM of 24 and 36 we can use
prime factorisation method. To find the LCM of two fractions say a/b and c/d, we have to use the formula: Multiples of 3 = 3, 6, 9,
12, 15, 18, 21, 24,… How do you find the least common denominator of two fractions?To find the least common denominator, list out the multiples of both denominators until you find the smallest multiple that is shared by both. Because 28 is the first shared multiple of 4 and 7, it must be the least common denominator for these two fractions.
What is the formula to find LCM of a fraction?LCM of fractions can be found using the simple formula LCM of Fractions = LCM of Numerators/HCF of Denominators.
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