LCM of 8 and 56 is 56. LCM is abbreviated as Least Common multiple or Lowest common multiple. LCM is the simplest method to find out the smallest common multiples between two or more than two numbers.
The LCM of 8 and 56 is the number that divides the number both 8 and 56 without leaving a remainder.
What is the LCM of 8 and 56?
The Least Common Multiple or Lowest Common Multiple of 8 and 56 is 56.
Usually, this is written as LCM(8, 56) = 56.
How to Find LCM of 8 and 56?
There are three regular methods for finding the LCM of 8 and 56.
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 8 and 56 Using Prime Factorisation Method
Prime factorization of 8 and 56 is (2 × 2 × 2 ) = 23 and ( 2 × 2 × 2 × 7 ) = 23 x 71 respectively .
LCM of 8 and 56 is obtained by multiplying prime factors raised to their highest power,
i.e 23 × 71 = 56.
Hence, the LCM of 8 and 56 by prime factorization is 56.
LCM of 8 and 56 by Division Method
To calculate the LCM of 8 and 56 by the division method, we will divide the numbers 8 and 56 by their prime factors. The product of these divisors gives us the LCM of 8 and 56
Let us see the steps to follow:
Step 1: Find 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. Bring down the number as it is, if it is not divisible by the prime number.
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
LCM of 8 and 56 by Listing Multiples
To calculate the LCM of 8 and 56, let us list the multiples of 8 and 56.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, …
Multiples of 56: 56, 112, …
Step 1: List out a few multiples of 8 and 56.
Step 2: Now the common multiples from the multiples of 8 and 56 are 56, 112, …
Step 3: The smallest common multiple of 8 and 56 is 56.
Hence the least common multiple of 8 and 56 = 56
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Solved Example
Example:
Find the smallest number that is divisible by 8 and 56 exactly.
Solution:
The smallest number that is divisible by 8 and 56 exactly is their LCM.
Therefore, the LCM of 8 and 56 is 56.
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