LCM of 6 and 28 is 84. From the multiples of 6 and 28, the number which is evenly divisible by the two numbers gives the LCM value. Least common multiple of 6 and 28 is the common multiple which is obtained using the multiplication operation. (6, 12, 18, 24, 30, ….) and (28, 56, 84, 112, 140, ….) are the multiples of 6 and 28. The LCM of two numbers is found using methods like listing multiples, prime factorization and division.
Also read: Least common multiple
What is LCM of 6 and 28?
The answer to this question is 84. The LCM of 6 and 28 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 28, is the smallest positive integer 84 which is divisible by both 6 and 28 with no remainder.
How to Find LCM of 6 and 28?
LCM of 6 and 28 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 28 Using Prime Factorisation Method
The prime factorisation of 6 and 28, respectively, is given by:
6 = 2¹ x 3¹
28 = 2 x 2 x 7 = 2² x 7¹
LCM (6, 28) = 84
LCM of 6 and 28 Using Division Method
We’ll divide the numbers (6, 28) by their prime factors to get the LCM of 6 and 28 using the division method (preferably common). The LCM of 6 and 28 is calculated by multiplying these divisors.
|
2 |
6 |
28 |
|
2 |
3 |
14 |
|
3 |
3 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (6, 28) = 84
LCM of 6 and 28 Using Listing the Multiples
To calculate the LCM of 6 and 28 by listing out the common multiples, list the multiples as shown below
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, ….
Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, …..
LCM (6, 28) = 84
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 6 and 28 Solved Examples
Question: The LCM and GCD of 6 and 28 is 84 and 2. Find the other number if one number is 6.
Solution:
Consider n as the other number
LCM x GCD = 6 x n
n = (LCM x GCD)/6
n = (28 x 6)/ 6
n = 28
Hence, the other number is 28.
Frequently Asked Questions on LCM of 6 and 28
List the methods used to determine the LCM of 6 and 28.
Using the prime factorisation method, what is the LCM of 6 and 28?
We should analyze the factors first to determine the LCM
6 = 2¹ x 3¹
28 = 2 x 2 x 7 = 2² x 7¹
LCM is the product of prime factors raised to the highest exponent among 6 and 28.
LCM of 6 and 28 = 84
Calculate the GCF if the LCM of 6 and 28 is 84.
LCM x GCF = 6 x 28
As the LCM = 84
84 x GCF = 168
GCF = 168/84 = 2
Comments