LCM of 48 and 56 is 336. Students will get a clear idea how the LCM of 48 and 56 can be found by reading this article. The least common multiple value of 48 and 56 is the smallest number which is evenly divisible by the two given numbers. The multiples of 48 are (48, 96, 144, 192, 240, 288, 336, 384, 432, ….) and the multiples of 56 are (56, 112, 168, 224, 280, 336, 392, 448, ….) respectively. Division method, Prime factorisation method and listing of the multiples are the most common methods used to find the LCM.
Also read: Least common multiple
What is LCM of 48 and 56?
The answer to this question is 336. The LCM of 48 and 56 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 48 and 56, is the smallest positive integer 336 which is divisible by both 48 and 56 with no remainder.
How to Find LCM of 48 and 56?
LCM of 48 and 56 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 48 and 56 Using Prime Factorisation Method
The prime factorisation of 48 and 56, respectively, is given by:
48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3¹
56 = 2 x 2 x 2 x 7 = 2³ x 7¹
LCM (48, 56) = 336
LCM of 48 and 56 Using Division Method
We’ll divide the numbers (48, 56) by their prime factors to get the LCM of 48 and 56 using the division method (preferably common). The LCM of 48 and 56 is calculated by multiplying these divisors.
|
2 |
48 |
56 |
|
2 |
24 |
28 |
|
2 |
12 |
14 |
|
2 |
6 |
7 |
|
3 |
3 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (48, 56) = 336
LCM of 48 and 56 Using Listing the Multiples
To calculate the LCM of 48 and 56 by listing out the common multiples, list the multiples as shown below
Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, 384, 432, ….
Multiples of 56 = 56, 112, 168, 224, 280, 336, 392, 448, ….
LCM (48, 56) = 336
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Video Lesson on Applications of LCM
LCM of 48 and 56 Solved Examples
Question: The product of two numbers is 2688. Calculate the LCM if the GCD is 8.
Solution:
It is given that
GCD = 8
Product of two numbers = 2688
We know that
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 2688/8
LCM = 336
Hence, the LCM is 336.
Frequently Asked Questions on LCM of 48 and 56
What is the LCM of 48 and 56?
We know that
Multiples of 48 = 48, 96, 144, 192, 240, 288, 336, 384, 432, ….
Multiples of 56 = 56, 112, 168, 224, 280, 336, 392, 448, ….
The smallest multiple exactly divisible by 48 and 56 is 336.
If the LCM of 48 and 56 is 336, find the GCF.
LCM x GCF = 48 x 56
Given
LCM of 48 and 56 is 336
336 x GCF = 2688
GCF = 2688/336 = 8
Mention the methods used to find the LCM of 48 and 56.
The methods used to find the LCM of 48 and 56 are
Division method
Prime Factorisation
Listing the multiples
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