LCM of 48 and 56
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 48 and 56 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 336 as output. Here you can check the answer for Find the LCM of 48 and 56.
What is LCM of 48 and 56
Given Numbers are 48, 56
We can find the LCM of 48, 56 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 48 and 56
Multiples of 48 =48,96,144,192,240,288,336,384,432,480,528,576,624,672,720,768,816,
Multiples of 56 =56,112,168,224,280,336,392,448,504,560,616,672,728,784,840,896,952,
Now, get the least common multiple of 48, 56 which is 336
So, the LCM of 48, 56 is 336.
Least Common Multiple (LCM) of 48 and 56 with the help of Prime Factorisation
One method for determining the LCM of 48 and 56 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 48's prime factorization:
| 2 | 48 |
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 48 are 2,3.
48 = 24×31
And this is 56's prime factorization:
| 2 | 56 |
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 56 are 2,7.
56 = 23×71
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,7
.24×31×71 = 336
This shows that the LCM of 48 and 56 is 336.
How to Calculate the LCM of 48 and 56 Using Common Multiples
The first step in determining the Least Common Multiple of 48 and 56 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 48 and 56:
Lets look at the first ten multiples of these numbers, 48 and 56:
48,96,144,192,240,288,336,384,432,816 are the first ten multiples of 48.
56,112,168,224,280,336,392,448,504,952 are the first ten multiples of 56.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 48 and 56, for example, are 576, 816, and 896. 336 is the least common multiple since it is the smallest.
48 and 56 have an LCM of 336.
Least Common Multiple of 48 and 56 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 56, than apply into the LCM equation.
GCF(48,56) = 8
LCM(48,56) = ( 48 × 56) / 8
LCM(48,56) = 2688 / 8
LCM(48,56) = 336
Related Least Common Multiples of 48
Related Least Common Multiples of 56
Frequently Asked Questions on LCM of 48 and 56
1. What is the LCM of 48 and 56?
The LCM of 48 and 56 is 336.
2. How to find the lowest common multiple of 48 and 56?
To find the lowest common multiple of 48 and 56, we have to get the multip;es of both numbers and identify the least common multiple in them which is 336.
3. What are the Factors of 48?
Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.
4. What are the Factors of 56?
Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.
5. How to Find the LCM of 48 and 56?Answer:
Least Common Multiple of 48 and 56 = 336
Step 1: Find the prime factorization of 48
48 = 2 x 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 56
56 = 2 x 2 x 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 336 = 2 x 2 x 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 48 and 56 is 336.