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