LCM of 8 and 56 - Detailed Explanation and Methods

Last Updated on May 30, 2024
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Exploring the LCM of 8 and 56 which is 56. LCM, the abbreviation for Least Common Multiple, is a simple method to identify the smallest common multiples between any two or even more numbers.

The LCM of 8 and 56 is a number that divides both numbers, 8 and 56, without leaving any remainder.

What is the LCM of 8 and 56?

The Least Common Multiple or Lowest Common Multiple of 8 and 56 is 56.

This is often represented as LCM(8, 56) = 56.

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How Do We Find the LCM of 8 and 56?

There are three common methods for finding the LCM of 8 and 56.

  • Using Prime Factorisation
  • Using the Division method
  • Listing the multiples

Finding the LCM of 8 and 56 Using Prime Factorisation

The prime factorization of 8 and 56 are (2 × 2 × 2 ) = 2 3 and ( 2 × 2 × 2 × 7 ) = 2 3 x 7 1 , respectively.

The LCM of 8 and 56 is obtained by multiplying the prime factors raised to their maximum power.

Hence, 2 3 × 7 1 = 56.

Therefore, the LCM of 8 and 56 by prime factorization is 56.

Finding the LCM of 8 and 56 Using the Division Method

To calculate the LCM of 8 and 56 using the division method, we divide the numbers 8 and 56 by their prime factors. The product of the divisors gives the LCM of 8 and 56.

Here are the steps to follow:

Step 1: Identify the smallest prime number that is a factor of at least one of the numbers, 8 and 56.

Step 2: If any of the given numbers, 8 or 56, is a multiple of 2, divide it by 2 and write the quotient below it. If the number is not divisible by the prime number, bring it down as is.

Step 3: Continue these steps until you get only 1’s in the last row.

The LCM of 8 and 56 by division method is 56.

2 8 56
2 4 28
2 2 14
7 1 7
1 1

LCM= 2 × 2 × 2 × 7 = 56

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Frequently Asked Questions

The LCM of 8 and 56 is 56.

GCF × LCM = 56 × 8.

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