Calculator Use
Use 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.
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
- Convert integers and mixed numbers to improper fractions
- Find the LCD of all the fractions
- Rewrite fractions as equivalent fractions using the LCD
Example Using the Lowest Common Denominator Calculator
Find the LCD of: 1 1/2, 3/8, 5/6, 3
- Convert integers and mixed numbers to improper fractions.
3/8 and 5/6 are already fractions so we can use those as they are written.
1 1/2 is the same as (1/1) + (1/2). Using the formula for adding fractions, ((n1*d2)+(n2*d1)) / (d1*d2), we get ((1*2)+(1*1)) / (1*2) = 3/2.
3 can be rewritten as a fraction as 3/1 - Equivalent fractions are: 3/2, 3/8, 5/6, 3/1
- Now find the least common denominator (LCD) (or the least common multiple (LCM) of the denominators)
- LCD = 24
- Rewriting the fractions as equivalent fractions using the LCD
- 36/24, 9/24, 20/24, 72/24
Related Calculators
We also have calculators for least common multiple, math with fractions, simplifying fractions, math with mixed numbers, and comparing fractions.
The first step to this method of finding the Least Common Multiple of 5 and 6 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 5 and 6:
What are the Multiples of 5?
What are the Multiples of 6?
Let’s take a look at the first 10 multiples for each of these numbers, 5 and 6:
First 10 Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
First 10 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 5 and 6 are 30, 60, 90. Because 30 is the smallest, it is the least common multiple.
The LCM of 5 and 6 is 30.
LCM of 5 and 6 is the smallest number among all common multiples of 5 and 6. The first few multiples of 5 and 6 are (5, 10, 15, 20, 25, 30, . . . ) and (6, 12, 18, 24, 30, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 6 - by prime factorization, by division method, and by listing multiples.
What is the LCM of 5 and 6?
Answer: LCM of 5 and 6 is 30.
Explanation:
The LCM of two non-zero integers, x(5) and y(6), is the smallest positive integer m(30) that is divisible by both x(5) and y(6) without any remainder.
Methods to Find LCM of 5 and 6
Let's look at the different methods for finding the LCM of 5 and 6.
- By Prime Factorization Method
- By Division Method
- By Listing Multiples
LCM of 5 and 6 by Prime Factorization
Prime factorization of 5 and 6 is (5) = 51 and (2 × 3) = 21 × 31 respectively. LCM of 5 and 6 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 =
30.
Hence, the LCM of 5 and 6 by prime factorization is 30.
LCM of 5 and 6 by Division Method
To calculate the LCM of 5 and 6 by the division method, we will divide the numbers(5, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 6.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 6. Write this prime number(2) on the left of the given numbers(5 and 6), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (5, 6) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
- Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 5 and 6 is the product of all prime numbers on the left, i.e. LCM(5, 6) by division method = 2 × 3 × 5 = 30.
LCM of 5 and 6 by Listing Multiples
To calculate the LCM of 5 and 6 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 6 (6, 12, 18, 24, 30, 36, . . . . )
- Step 2: The common multiples from the multiples of 5 and 6 are 30, 60, . . .
- Step 3: The smallest common multiple of 5 and 6 is 30.
∴ The least common multiple of 5 and 6 = 30.
☛ Also Check:
- LCM of 54 and 60 - 540
- LCM of 35 and 60 - 420
- LCM of 2 and 12 - 12
- LCM of 8, 9 and 12 - 72
- LCM of 12, 16, 24 and 36 - 144
- LCM of 12 and 25 - 300
- LCM of 54 and 90 - 270
FAQs on LCM of 5 and 6
What is the LCM of 5 and 6?
The LCM of 5 and 6 is 30. To find the least common multiple of 5 and 6, we need to find the multiples of 5 and 6 (multiples of 5 = 5, 10, 15, 20 . . . . 30; multiples of 6 = 6, 12, 18, 24 . . . . 30) and choose the smallest multiple that is exactly divisible by 5 and 6, i.e., 30.
If the LCM of 6 and 5 is 30, Find its GCF.
LCM(6, 5) × GCF(6, 5) = 6 × 5
Since the LCM of 6 and 5 = 30
⇒ 30 × GCF(6, 5) = 30
Therefore, the greatest common factor = 30/30 = 1.
What are the Methods to Find LCM of 5 and 6?
The commonly used methods to find the LCM of 5 and 6 are:
- Listing Multiples
- Prime Factorization Method
- Division Method
What is the Relation Between GCF and LCM of 5, 6?
The following equation can be used to express the relation between GCF and LCM of 5 and 6, i.e. GCF × LCM = 5 × 6.
Which of the following is the LCM of 5 and 6? 3, 32, 35, 30
The value of LCM of 5, 6 is the smallest common multiple of 5 and 6. The number satisfying the given condition is 30.