LCM of 8 and 28 is 56. The smallest number divisible evenly among the multiples of the numbers 8 and 28 gives the LCM. The common multiples of the two numbers helps you find the least common multiple of 8 and 28. (8, 16, 24, 32, 40, 48, ….) and (28, 56, 84, 112, 140, 168,….) are the multiples of 8 and 28. The LCM of the given numbers using the prime factorisation method, division method and by listing out the multiples is explained briefly in this article.
Also read: Least common multiple
What is LCM of 8 and 28?
The answer to this question is 56. The LCM of 8 and 28 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 28, is the smallest positive integer 56 which is divisible by both 8 and 28 with no remainder.
How to Find LCM of 8 and 28?
LCM of 8 and 28 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 28 Using Prime Factorisation Method
The prime factorisation of 8 and 28, respectively, is given by:
8 = 2 x 2 x 2 = 2³
28 = 2 x 2 x 7 = 2² x 7¹
LCM (8, 28) = 56
LCM of 8 and 28 Using Division Method
We’ll divide the numbers (8, 28) by their prime factors to get the LCM of 8 and 28 using the division method (preferably common). The LCM of 8 and 28 is calculated by multiplying these divisors.
|
2 |
8 |
28 |
|
2 |
4 |
14 |
|
2 |
2 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (8, 28) = 56
LCM of 8 and 28 Using Listing the Multiples
To calculate the LCM of 8 and 28 by listing out the common multiples, list the multiples as shown below
|
Multiples of 8 |
Multiples of 28 |
|
8 |
28 |
|
16 |
56 |
|
24 |
74 |
|
32 |
112 |
|
40 |
140 |
|
48 |
168 |
|
56 |
196 |
|
64 |
224 |
LCM (8, 28) = 56
Related Articles
Video Lesson on Applications of LCM
LCM of 8 and 28 Solved Examples
Question: The LCM and GCD of two numbers are 56 and 4. If one number is 28, determine the other.
Solution:
Consider b as the other number
We know that
LCM x GCD = 28 x b
b = (LCM X GCD)/28
b = (56 x 4)/ 28
b = 8
Hence, the other number is 8.
Frequently Asked Questions on LCM of 8 and 28
Find the LCM of 8 and 28.
The LCM of 8 and 28 is 56.
The smallest multiple exactly divisible by 8 and 28 should be found.
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, …
Multiples of 28 = 28, 56, 84, 112, 140, ….
The smallest common multiple exactly divisible by 8 and 28 is 56.
List the methods used to find the LCM of 8 and 28.
What is the GCF if the LCM of 8 and 28 is 56?
LCM x GCF = 8 x 28
Given
LCM of 8 and 28 = 56
56 x GCF = 224
GCF = 224/56 = 4
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