LCM of 16 and 56 is 112. 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 16 and 56, is the smallest number among all the common multiples of 16 and 56.
What is the LCM of 16 and 56?
The Least Common Multiple or Lowest Common Multiple of 16 and 56 is 112.
How to Find LCM of 16 and 56?
Let us see the different methods for finding the LCM of 16 and 56. They are:
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 16 and 56 Using Prime Factorisation Method
Prime factorization of 16 and 56 are (2 × 2 × 2 × 2) = 24 and ( 2 × 2 × 2 × 7 ) = 23× 71 .
LCM of 16 and 56 is obtained by multiplying prime factors raised to their respective highest power.
i.e., 24 × 71 = 112.
Hence, the LCM of 16 and 56 by prime factorization is 112.
LCM of 16 and 56 by Division Method
To calculate the LCM of 16 and 56 by the division method, we will divide the numbers 16 and 56 by their prime factors. The product of these divisors gives the LCM of 16 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, 16 and 56.
Step 2: If any of the given numbers 16 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 16 and 56 by division method is 112.
| 2 | 16 | 56 |
| 2 | 8 | 28 |
| 2 | 4 | 14 |
| 2 | 2 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
LCM= 2 × 2 × 2 × 2 × 7 = 112
LCM of 16 and 56 by Listing Multiples
To calculate the LCM of 16 and 56, first, list the multiples of 16 and 56.
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, …
Multiples of 56: 56, 112, 168, 224, 280, 336, …
Step 1: List out a few multiples of 16 and 56.
Step 2: Now the common multiples from the multiples of 16 and 56 are 112, 224, ..
Step 3: The smallest common multiple of 16 and 56 is 112.
Hence the least common multiple of 16 and 56 = 112.
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Solved Example
Example:
Find the smallest number that is divisible by 16 and 56 exactly.
Solution:
The smallest number that is divisible by 16 and 56 exactly is their LCM.
Therefore, the LCM of 16 and 56 is 112.
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