What is the denominator of 6 and 7?

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

1. Convert integers and mixed numbers to improper fractions
2. Find the LCD of all the fractions
3. 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)
• 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.

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 6 and 7 is 42.

LCM(6,7) = 42

Least Common Multiple of 6 and 7 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 7, than apply into the LCM equation.

GCF(6,7) = 1 LCM(6,7) = ( 6 × 7) / 1 LCM(6,7) = 42 / 1

LCM(6,7) = 42

Least Common Multiple (LCM) of 6 and 7 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 7. First we will calculate the prime factors of 6 and 7.

Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 21 × 31

Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 71

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 7.

LCM(6,7) = 21 × 31 × 71
LCM(6,7) = 42

The first step to this method of finding the Least Common Multiple of 6 and 7 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, 6 and 7:

What are the Multiples of 6?

What are the Multiples of 7?

Let’s take a look at the first 10 multiples for each of these numbers, 6 and 7:

First 10 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

First 10 Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

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 6 and 7 are 42, 84, 126. Because 42 is the smallest, it is the least common multiple.

The LCM of 6 and 7 is 42.

LCM of 6 and 7 is the smallest number among all common multiples of 6 and 7. The first few multiples of 6 and 7 are (6, 12, 18, 24, 30, 36, . . . ) and (7, 14, 21, 28, 35, 42, 49, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 7 - by division method, by prime factorization, and by listing multiples.

What is the LCM of 6 and 7?

Answer: LCM of 6 and 7 is 42.

Explanation:

The LCM of two non-zero integers, x(6) and y(7), is the smallest positive integer m(42) that is divisible by both x(6) and y(7) without any remainder.

Methods to Find LCM of 6 and 7

The methods to find the LCM of 6 and 7 are explained below.

• By Division Method
• By Listing Multiples
• By Prime Factorization Method

LCM of 6 and 7 by Division Method

To calculate the LCM of 6 and 7 by the division method, we will divide the numbers(6, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 7.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 7. Write this prime number(2) on the left of the given numbers(6 and 7), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 7) 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 6 and 7 is the product of all prime numbers on the left, i.e. LCM(6, 7) by division method = 2 × 3 × 7 = 42.

LCM of 6 and 7 by Listing Multiples

To calculate the LCM of 6 and 7 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, . . . ) and 7 (7, 14, 21, 28, 35, 42, 49, . . . . )
• Step 2: The common multiples from the multiples of 6 and 7 are 42, 84, . . .
• Step 3: The smallest common multiple of 6 and 7 is 42.

∴ The least common multiple of 6 and 7 = 42.

LCM of 6 and 7 by Prime Factorization

Prime factorization of 6 and 7 is (2 × 3) = 21 × 31 and (7) = 71 respectively. LCM of 6 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 71 = 42.
Hence, the LCM of 6 and 7 by prime factorization is 42.

☛ Also Check:

1. Example 1: Find the smallest number that is divisible by 6 and 7 exactly.

   Solution:

   The smallest number that is divisible by 6 and 7 exactly is their LCM.
   ⇒ Multiples of 6 and 7:

   • Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, . . . .
   • Multiples of 7 = 7, 14, 21, 28, 35, 42, . . . .

   Therefore, the LCM of 6 and 7 is 42.

2. Example 2: Verify the relationship between GCF and LCM of 6 and 7.

   Solution:

   The relation between GCF and LCM of 6 and 7 is given as, LCM(6, 7) × GCF(6, 7) = Product of 6, 7

   Prime factorization of 6 and 7 is given as, 6 = (2 × 3) = 21 × 31 and 7 = (7) = 71

   LCM(6, 7) = 42 GCF(6, 7) = 1 LHS = LCM(6, 7) × GCF(6, 7) = 42 × 1 = 42 RHS = Product of 6, 7 = 6 × 7 = 42 ⇒ LHS = RHS = 42

   Hence, verified.

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The LCM of 6 and 7 is 42. To find the least common multiple of 6 and 7, we need to find the multiples of 6 and 7 (multiples of 6 = 6, 12, 18, 24 . . . . 42; multiples of 7 = 7, 14, 21, 28 . . . . 42) and choose the smallest multiple that is exactly divisible by 6 and 7, i.e., 42.

What are the Methods to Find LCM of 6 and 7?

The commonly used methods to find the LCM of 6 and 7 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

How to Find the LCM of 6 and 7 by Prime Factorization?

To find the LCM of 6 and 7 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (7 = 7). LCM of 6 and 7 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 7.
⇒ LCM of 6, 7 = 21 × 31 × 71 = 42.

What is the Relation Between GCF and LCM of 6, 7?

The following equation can be used to express the relation between GCF and LCM of 6 and 7, i.e. GCF × LCM = 6 × 7.

If the LCM of 7 and 6 is 42, Find its GCF.

LCM(7, 6) × GCF(7, 6) = 7 × 6 Since the LCM of 7 and 6 = 42 ⇒ 42 × GCF(7, 6) = 42

Therefore, the GCF = 42/42 = 1.