LCM of 20 and 50

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.

lcm of 20 and 50

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

HCF and LCM

Least Common Multiple (LCM)

LCM Calculator

LCM with Examples

LCM Formula

LCM of Two Numbers

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

Q1

What is the LCM of 20 and 50?

The LCM of 20 and 50 is 100.
Q2

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

Q3

Is 150 the LCM of 20 and 50?

No. The LCM of 20 and 50 is 100.
Q4

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.

Q5

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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