LCM of 10, 15 and 20 is 60. The least common multiple is a method to find the smallest common multiple between any two or more numbers. Students are recommended to learn the LCM concept thoroughly to get more marks in the exams. Least Common Multiple (LCM) is designed by experts in a simple and lucid manner to provide the best reference material for students. Learn how to calculate the least common multiple of 10, 15 and 20 using the prime factorisation, division method and listing multiples with simple steps in this article.
What is LCM of 10, 15 and 20?
The answer to this question is 60.
How to Find LCM of 10, 15 and 20?
The below methods are used to find the LCM of 10, 15 and 20:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10, 15 and 20 Using Prime Factorisation Method
By prime factorisation method, we can write 10, 15 and 20 as the product of prime numbers, such that;
10 = 2 × 5
15 = 3 × 5
20 = 2 × 2 × 5
LCM (10, 15, 20) = 2 × 2 × 3 × 5 = 60
LCM of 10, 15 and 20 Using Division Method
In this method, we divide the numbers 10, 15 and 20 by their prime factors to find their LCM. The product of these divisors denotes the least common multiple of 10, 15 and 20. This can be shown as below.
| 2 | 10 | 15 | 20 |
| 2 | 5 | 15 | 10 |
| 3 | 5 | 15 | 5 |
| 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 |
No more further division can be done.
Therefore, LCM (10, 15, 20) = 2 × 2 × 3 × 5 = 60
LCM of 10, 15 and 20 Using Listing the Multiples
Here we list out the multiples of 10, 15 and 20 to calculate their least common multiple as shown below:
| Multiples of 10 | Multiples of 15 | Multiples of 20 |
| 10 | 15 | 20 |
| 20 | 30 | 40 |
| 30 | 45 | 60 |
| 40 | 60 | 80 |
| 50 | 75 | 100 |
| 60 | 90 | 120 |
| 70 | 105 | 140 |
| 80 | 120 | 160 |
| 90 | 135 | 180 |
| 100 | 150 | 200 |
LCM (10, 15, 20) = 60
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by 10, 15 and 20?
Solution: The smallest number that is divisible by 10, 15 and 20 is 60.
Q. 2: Find the LCM of 10, 15 and 20 by division method.
Solution: We can find the LCM of 10, 15 and 20 by division method as below
| 2 | 10 | 15 | 20 |
| 2 | 5 | 15 | 10 |
| 3 | 5 | 15 | 5 |
| 5 | 5 | 5 | 5 |
| x | 1 | 1 | 1 |
LCM (10, 15, 20) = 2 × 2 × 3 × 5 = 60
Hence the LCM of 10,15 and 20 is 60.
Frequently Asked Questions on LCM of 10, 15 and 20
What is the LCM of 10, 15 and 20?
Name the methods used to find the LCM of 10, 15 and 20.
The methods used to find the LCM of 10, 15 and 20 are
Prime factorisation
Division method
Listing the multiples
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