LCM of 56 and 96 is 672. LCM or least common multiple is the simplest method to find out the smallest common multiple between two or more than two numbers. Here the LCM of 56 and 96 is 672, where 672 is the smallest common multiple for numbers 56 and 96.
What is the LCM of 56 and 96?
The Least Common Multiple or Lowest Common Multiple of 56 and 96 is 672.
How to Find LCM of 56 and 96?
LCM of 56 and 96 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 56 and 96 Using Prime Factorisation Method
Let us find the LCM of 56 and 96 by the Prime factorization method stepwise:
Step 1: Find all the prime factors of numbers 56 and 96
Step 2: Now, list down all the prime numbers found,
Prime factorisation of 56 and 96 is as follows:
56 = 23 × 71
96 = 25 × 31
Step 3: LCM of 56 and 96 can be obtained by multiplying prime factors raised to their highest power.
i.e., 25 × 31 × 71 = 672
Hence, the LCM of 56 and 96 by prime factorization is 672.
LCM of 56 and 96 by division method
To Calculate the LCM of 56 and 96
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 56 and 96.
Step 2: If any of the numbers either 56 or 96 is a multiple of 2, divide it by 2 and write the quotient below it. If any number is not divisible by the prime number then bring it below.
Step 3: Continue this process until you get only 1s in the last row.
The LCM of 56 and 96 by division method = 2 × 2 × 2 × 2 × 2 × 3 × 7 = 672.
| 2 | 56 | 96 |
| 2 | 28 | 48 |
| 2 | 14 | 24 |
| 2 | 7 | 12 |
| 2 | 7 | 6 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| 1 | 1 |
LCM of 56 and 96 by Listing Multiples
At first, calculate the LCM of 56 and 96 by listing out the common multiples, let us follow the below steps.
Step 1: List a few multiples of 56 and 96 as shown below.
56 – 56, 112, 168, 224, 280, 336, …
96 – 96, 192, 288, 384, 480, 576, …
Step 2: The common multiples from the multiples of 56 and 96 are 672, …
Step 3: The common multiple of 56 and 96 = 672
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Solved Example
Example:
What is the smallest number that is divisible by 56 and 96 exactly?
Solution:
The smallest number that is divisible by 56 and 96 exactly is their LCM.
Therefore, the LCM of 56 and 96 is 672.
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