LCM of 6 and 30 is 30. Know more on how the least common multiple of 6 and 30 is calculated considering the common multiples. The multiples of 6 are (6, 12, 18, 24, 30, 36, ….) and the multiples of 30 are (30, 60, 90, 120, 150, 180, ,….). The LCM of two numbers using the prime factorisation method, by listing out the multiples and division methods, is explained here in an interesting way.
Also read: Least common multiple
What is LCM of 6 and 30?
The answer to this question is 30. The LCM of 6 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6 and 30, is the smallest positive integer 30 which is divisible by both 6 and 30 with no remainder.
How to Find LCM of 6 and 30?
LCM of 6 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 30 Using Prime Factorisation Method
The prime factorisation of 6 and 30, respectively, is given by:
6 = 2 × 3 = 2¹× 3¹
30 = 2 × 3 × 5 = 2¹× 3¹× 5¹
LCM (6, 30) = 30
LCM of 6 and 30 Using Division Method
We’ll divide the numbers (6, 30) by their prime factors to get the LCM of 6 and 30 using the division method (preferably common). The LCM of 6 and 30 is calculated by multiplying these divisors.
|
2 |
6 |
30 |
|
3 |
3 |
15 |
|
5 |
1 |
5 |
|
× |
1 |
1 |
No further division can be done.
Hence, LCM (6, 30) = 30
LCM of 6 and 30 Using Listing the Multiples
To calculate the LCM of 6 and 30 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 6 |
Multiples of 30 |
|
6 |
30 |
|
12 |
60 |
|
18 |
90 |
|
24 |
120 |
|
30 |
150 |
|
36 |
180 |
The smallest common multiple of 6 and 30 is 30.
Therefore LCM (6, 30) = 30
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 30 Solved Examples
Question: If the product of two numbers is 180 and the GCD is 6, find the LCM.
Solution:
It is given that
Product of two numbers = 180
GCD = 6
We know that
LCM × GCD = Product of two numbers
LCM = Product/GCD
LCM = 180/6
LCM = 30
Hence, the LCM is 30.
Frequently Asked Questions on LCM of 6 and 30
What is the LCM of 6 and 30?
What methods are used to get the LCM of 6 and 30?
Find the GCF if the LCM of 6 and 30 is 30.
LCM × GCF = 6 × 30
Given
LCM of 6 and 30 = 30
30 × GCF = 180
GCF = 180/30 = 6
By listing the multiples, find the LCM of 6 and 30.
By listing the multiples
Multiples of 6 = 6, 12, 18, 24, 30, 36, ….
Multiples of 30 = 30, 60, 90, 120, 150, 180, …..
LCM = 30
Using prime factorisation, calculate the LCM of 6 and 30.
Using prime factorisation,
6 = 2 × 3
30 = 2 × 3 × 5
LCM (6, 30) = 30
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