LCM of 20, 25 and 30

LCM of 20, 25 and 30 is 300. The common multiples of 20, 25 and 30 divisible evenly by the given numbers is the LCM. Least common multiples of 20, 25 and 30 can be found in the common multiples. (20, 40, 60, 80, 100, ….), (25, 50, 75, 100, 125, ……) and (30, 60, 90, 120, 150, 180,….) are the multiples of 20, 25 and 30. Students can use the methods such as division, prime factorisation and listing of multiples to get the LCM value.

Also read: Least common multiple

What is LCM of 20, 25 and 30?

The answer to this question is 300. The LCM of 20, 25 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 20, 25 and 30, is the smallest positive integer 300 divisible by both 20, 25 and 30 with no remainder.

lcm of 20 25 and 30

How to Find LCM of 20, 25 and 30?

LCM of 20, 25 and 30 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 20, 25 and 30 Using Prime Factorisation Method

The prime factorisation of 20, 25 and 30, respectively, is given by:

20 = 2 x 2 x 5 = 2² x 5¹

25 = 5 x 5 = 5² 

30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹

LCM (20, 25, 30) = 300

LCM of 20, 25 and 30 Using Division Method

We’ll divide the numbers (20, 25, 30) by their prime factors to get the LCM of 20, 25 and 30 using the division method (preferably common). The LCM of 20, 25 and 30 is calculated by multiplying these divisors.

2 20 25 30
2 10 25 15
3 5 25 15
5 5 25 5
5 1 5 1
1 1 1

No further division can be done. 

Hence, LCM (20, 25, 30) = 300

LCM of 20, 25 and 30 Using Listing the Multiples

To calculate the LCM of 20, 25 and 30 by listing out the common multiples, list the multiples as shown below

Multiples of 20 Multiples of 25 Multiples of 30
20 25 30
40 50 60
60 75 90
80 100 120
100 125 150
120 150 180
140 175 210
160 200 240
180 225 270
200 250 300
220 275
240 300
260
280
300

LCM (20, 25, 30) = 300

Related Articles

Video Lesson on Applications of LCM

LCM of 20, 25 and 30 Solved Example

Which is the smallest number divisible by 20, 25 and 30 exactly?

Solution:

The smallest number divisible by 20, 25 and 30 exactly is the LCM.

Multiples of 20 = 20, 40, 60, 80, 100, ….

Multiples of 25 = 25, 50, 75, 100, 125, …..

Multiples of 30 = 30, 60, 90, 120, 150, 180, ….

Hence, the LCM is 300.

Frequently Asked Questions on LCM of 20, 25 and 30

Q1

How to find the LCM of 20, 25 and 30?

The LCM of 20, 25 and 30 is 300. The multiples of 20, 25 and 30 which are common and exactly divisible by the given numbers helps to find the LCM.
Q2

What are the methods used to determine the LCM of 20, 25 and 30?

The methods that can be used to determine the LCM of 20, 25 and 30 are Prime Factorization Method, Division Method and Listing multiples.
Q3

Using prime factorization, find the LCM of 20, 25 and 30.

Using prime factorization,

20 = 2 x 2 x 5 = 2² x 5¹

25 = 5 x 5 = 5²

30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹

LCM (20, 25, 30) = 300

Therefore, the LCM of 20, 25 and 30 is 300.

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