LCM of 20 and 50 is 100. In Mathematics, LCM stands for Least Common Multiple. It is defined as the smallest common multiple of two or more numbers. By referring to the article Prime Factorisation and Division Method for HCF and LCM, students will learn the technique of finding LCM and HCF of given numbers in a comprehensive manner. Let us look at how to determine the least common multiple of 20 and 50 using simple steps in this article.
What is LCM of 20 and 50?
The Least Common Multiple of 20 and 50 is 100.
How to Find LCM of 20 and 50?
The LCM of 20 and 50 can be determined by using the following methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20 and 50 Using Prime Factorisation Method
In the prime factorisation method, we multiply the prime factors raised to their respective highest power to determine the least common multiple of 20 and 50.
20 = 2 × 2 × 5
50 = 2 × 5 × 5
LCM (20, 50) = 2 × 2 × 5 × 5 = 100
LCM of 20 and 50 Using Division Method
Here, we divide the numbers 20 and 50 by their prime factors until we get the result as one in the complete row to find the least common multiple of 20 and 50. The product of these divisors depicts the least common multiple of 20 and 50.
| 2 | 20 | 50 |
| 2 | 10 | 25 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (20, 50) = 2 × 2 × 5 × 5 = 100
LCM of 20 and 50 Using Listing the Multiples
In this method, by listing the multiple of 20 and 50, we can find the least common multiple of 20 and 50. The multiples of 20 and 50 are shown in the below table.
| Multiples of 20 | Multiples of 50 |
| 20 | 50 |
| 40 | 100 |
| 60 | 150 |
| 80 | 200 |
| 100 | 250 |
| 120 | 300 |
| 140 | 350 |
| 160 | 400 |
LCM (20, 50) = 100
Related Articles
Video Lesson on Applications of LCM
Solved Examples
Q. 1: How do you find the LCM of 20 and 50 using the division method?
Solution: We can find the LCM of 20 and 50 using the division method as shown below
| 2 | 20 | 50 |
| 2 | 10 | 25 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
LCM (20, 50) = 2 × 2 × 5 × 5 = 100
Therefore the least common multiple of 20 and 50 is 100.
Q. 2: Find the smallest number that is divisible by both 20 and 50.
Solution: First list the multiples of 20 and 50
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, 160, …….
Multiples of 50 = 50, 100, 150, 200, 250, 300, 350, 400, …..
Here the LCM is 100.
Hence 100 is the smallest number that is divisible by both 20 and 50.
Frequently Asked Questions on LCM of 20 and 50
What is the LCM of 20 and 50?
What are the methods used to find the LCM of 20 and 50?
The methods to find the LCM of 20 and 50 are as follows:
Prime Factorisation
Division Method
Listing the multiples
Is 150 the LCM of 20 and 50?
Find the GCF if the LCM of 20 and 50 is 100.
We know that
LCM × GCF = 20 × 50
Given LCM of 20 and 50 is 100
100 × GCF = 1000
GCF = 10
Thus the GCF is 10.
Write the relation between GCF and LCM of 20 and 50.
The relation between GCF and LCM of 20 and 50 is
GCF × LCM = 20 × 50
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