LCM of 6 and 10 is 30. The technique of finding the smallest common multiple between two or more numbers is defined as LCM. The full form of LCM is least common multiple or lowest common multiple. Students can grasp the knowledge based on LCM by using the article Lowest Common Multiple (LCM) prepared by expert faculty with the aim to provide the best reference guide for students. Let us learn how to find the least common multiple of 6 and 10 using a simple method in this article.
What is LCM of 6 and 10?
The answer to this question is 30.
How to Find LCM of 6 and 10?
We can find the LCM of 6 and 10 with the help of the following methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 10 Using Prime Factorisation Method
By prime factorisation method, we can write 6 and 10 as the product of prime numbers, such that;
6 = 2 × 3
10 = 2 × 5
LCM (6, 10) = 2 × 3 × 5 = 30
LCM of 6 and 10 Using Division Method
Here, we divide the numbers 6 and 10 by their prime factors to determine their LCM. The product of these divisors shows the least common multiple of 6 and 10.
| 2 | 6 | 10 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (6, 10) = 2 × 3 × 5 = 30
LCM of 6 and 10 Using Listing the Multiples
To determine the least common multiple of 6 and 10 using listing multiples, we list out the multiples of 6 and 10 as shown below.
| Multiples of 6 | Multiples of 10 |
| 6 | 10 |
| 12 | 20 |
| 18 | 30 |
| 24 | 40 |
| 30 | 50 |
| 36 | 60 |
| 42 | 70 |
LCM (6, 10) = 30
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Calculate the LCM if the product of two numbers is 60 and their GCD is 2.
Solution: Given,
GCD = 2
Product of numbers = 60
We know that,
LCM × GCD = Product of numbers
LCM = Product of numbers/GCD
LCM = 60/2
LCM = 30
Therefore the LCM is 30.
Q. 2: Find the LCM of 6 and 10 using the listing multiples.
Solution: First list out the multiples of 6 and 10.
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, …..
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70,…..
Here the LCM is 30.
Thus the LCM of 6 and 10 is 30.
Frequently Asked Questions on LCM of 6 and 10
What is the LCM of 6 and 10?
Name the methods used to find the LCM of 6 and 10.
The methods used to find the LCM of 6 and 10 are
Prime Factorisation
Division Method
Listing the multiples
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