LCM of 20 and 30 is 60. The smallest number among all frequent multiples of 20 and 30 is the LCM of 20 and 30. (20, 40, 60, 80, etc.) and (30, 60, 90, 120, 150, 180, etc.) are the first few multiples of 20 and 30. To find the LCM of 20 and 30, there are three typical methods: listing multiples, division method, and prime factorization. The LCM of any two integers is the value that is evenly divided by the two values in mathematics.
Also read: Least common multiple
What is LCM of 20 and 30?
The answer to this question is 60. The LCM of 20 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 20 and 30, is the smallest positive integer 60 which is divisible by both 20 and 30 with no remainder.
How to Find LCM of 20 and 30?
LCM of 20 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20 and 30 Using Prime Factorisation Method
The prime factorisation of 20 and 30, respectively, is given by:
20 = (2 × 2 × 5) = 22 × 51 and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (20, 30) = 60
LCM of 20 and 30 Using Division Method
We’ll divide the numbers (20, 30) by their prime factors to get the LCM of 20 and 30 using the division method (preferably common). The LCM of 20 and 30 is calculated by multiplying these divisors.
| 2 | 20 | 30 |
| 2 | 10 | 30 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| 1 | 1 |
No further division can be done.
Hence, LCM (20, 30) = 60
LCM of 20 and 30 Using Listing the Multiples
To calculate the LCM of 20 and 30 by listing out the common multiples, list the multiples as shown below
| Multiples of 20 | Multiples of 30 |
| 20 | 30 |
| 40 | 60 |
| 60 | 90 |
| 80 | 120 |
| 100 | 150 |
The smallest common multiple of 20 and 30 is 60.
LCM (20, 30) = 60
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Video Lesson on Applications of LCM
LCM of 20 and 30 Solved Example
The product of two numbers is 600. If their GCD is 10, what is their LCM?
Solution:
Given: GCD = 10
product of numbers = 600
LCM × GCD = product of numbers
LCM = Product/GCD = 600/10
Therefore, the LCM is 60.
The probable combination for the given case is LCM(20, 30) = 60.
Frequently Asked Questions on LCM of 20 and 30
If the LCM of 30 and 20 is 60, Find its GCF.
Since the LCM of 30 and 20 = 60
⇒ 60 × GCF(30, 20) = 600
Therefore, the GCF (greatest common factor) = 600/60 = 10.
Which of the following is the LCM of 20 and 30? 60, 10, 36, 40
What are the Methods to Find LCM of 20 and 30?
Listing Multiples
Division Method
Prime Factorization Method
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