What is the least common multiple of 8 and 7?

Least Common Multiple (LCM) of 8 and 7

Step 1) First we find and list the prime factors of 8 and 7 (Prime Factorization):

Prime Factors of 8: 2, 2, 2 Prime Factors of 7: 7 Step 2) Then we look at the frequency of the prime factors as they appear in each set above. List each prime factor the greatest number of times it occurs in either sets:

2, 2, 2, 7 Step 3) Finally, we multiply the prime numbers from Step 2 together.

2 x 2 x 2 x 7 = 56 That's it. The Least Common Multiple (LCM) of 8 and 7 is 56.

Least Common Multiple (LCM) of 8 and 8

LCM(8, 7) = 23×7 = 56

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The first step to this method of finding the Least Common Multiple of 8 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, 8 and 7:

What are the Multiples of 8?

What are the Multiples of 7?

Let’s take a look at the first 10 multiples for each of these numbers, 8 and 7:

First 10 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

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 8 and 7 are 56, 112, 168. Because 56 is the smallest, it is the least common multiple.

The LCM of 8 and 7 is 56.

The LCM of 7 and 8 is 56.

Steps to find LCM

1. Find the prime factorization of 7
   7 = 7
2. Find the prime factorization of 8
   8 = 2 × 2 × 2
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 2 × 2 × 2 × 7

4. LCM = 56

MathStep (Works offline)

Find least common multiple (LCM) of: 14 & 16 21 & 24 35 & 40 49 & 56 14 & 8 7 & 16 21 & 8 7 & 24 35 & 8 7 & 40 49 & 8 7 & 56

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

LCM of 7 and 8 is the smallest number among all common multiples of 7 and 8. The first few multiples of 7 and 8 are (7, 14, 21, 28, . . . ) and (8, 16, 24, 32, 40, 48, 56, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 8 - by listing multiples, by prime factorization, and by division method.

What is the LCM of 7 and 8?

Answer: LCM of 7 and 8 is 56.

Explanation:

The LCM of two non-zero integers, x(7) and y(8), is the smallest positive integer m(56) that is divisible by both x(7) and y(8) without any remainder.

Methods to Find LCM of 7 and 8

Let's look at the different methods for finding the LCM of 7 and 8.

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

LCM of 7 and 8 by Prime Factorization

Prime factorization of 7 and 8 is (7) = 71 and (2 × 2 × 2) = 23 respectively. LCM of 7 and 8 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 71 = 56.
Hence, the LCM of 7 and 8 by prime factorization is 56.

LCM of 7 and 8 by Division Method

To calculate the LCM of 7 and 8 by the division method, we will divide the numbers(7, 8) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 8.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 8. Write this prime number(2) on the left of the given numbers(7 and 8), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (7, 8) 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 7 and 8 is the product of all prime numbers on the left, i.e. LCM(7, 8) by division method = 2 × 2 × 2 × 7 = 56.

LCM of 7 and 8 by Listing Multiples

To calculate the LCM of 7 and 8 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, . . . ) and 8 (8, 16, 24, 32, 40, 48, 56, . . . . )
• Step 2: The common multiples from the multiples of 7 and 8 are 56, 112, . . .
• Step 3: The smallest common multiple of 7 and 8 is 56.

∴ The least common multiple of 7 and 8 = 56.

☛ Also Check:

1. Example 1: The product of two numbers is 56. If their GCD is 1, what is their LCM?

   Solution:

   Given: GCD = 1 product of numbers = 56 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 56/1 Therefore, the LCM is 56.

   The probable combination for the given case is LCM(7, 8) = 56.

Show Solution >

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The LCM of 7 and 8 is 56. To find the LCM of 7 and 8, we need to find the multiples of 7 and 8 (multiples of 7 = 7, 14, 21, 28 . . . . 56; multiples of 8 = 8, 16, 24, 32 . . . . 56) and choose the smallest multiple that is exactly divisible by 7 and 8, i.e., 56.

What is the Least Perfect Square Divisible by 7 and 8?

The least number divisible by 7 and 8 = LCM(7, 8)
LCM of 7 and 8 = 2 × 2 × 2 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 7 and 8 = LCM(7, 8) × 2 × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.

What is the Relation Between GCF and LCM of 7, 8?

The following equation can be used to express the relation between GCF and LCM of 7 and 8, i.e. GCF × LCM = 7 × 8.

If the LCM of 8 and 7 is 56, Find its GCF.

LCM(8, 7) × GCF(8, 7) = 8 × 7 Since the LCM of 8 and 7 = 56 ⇒ 56 × GCF(8, 7) = 56

Therefore, the GCF (greatest common factor) = 56/56 = 1.

How to Find the LCM of 7 and 8 by Prime Factorization?

To find the LCM of 7 and 8 using prime factorization, we will find the prime factors, (7 = 7) and (8 = 2 × 2 × 2). LCM of 7 and 8 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 8.
⇒ LCM of 7, 8 = 23 × 71 = 56.