LCM of 8 and 30 is 120. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 8 and 30 is the LCM of 8 and 30. (8, 16, 24, 32, etc.) and (30, 60, 90, 120, 150, 180, etc.) are the first few multiples of 8 and 30. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 8 and 30?
The answer to this question is 120. The LCM of 8 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 30, is the smallest positive integer 120 which is divisible by both 8 and 30 with no remainder.
How to Find LCM of 8 and 30?
LCM of 8 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 30 Using Prime Factorisation Method
The prime factorisation of 8 and 30, respectively, is given by:
8 = (2 × 2 × 2) = 23 and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (8, 30) = 120
LCM of 8 and 30 Using Division Method
We’ll divide the numbers (8, 30) by their prime factors to get the LCM of 8 and 30 using the division method (preferably common). The LCM of 8 and 30 is calculated by multiplying these divisors.
| 2 | 8 | 30 |
| 2 | 4 | 15 |
| 2 | 2 | 15 |
| 3 | 1 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (8, 30) = 120
LCM of 8 and 30 Using Listing the Multiples
To calculate the LCM of 8 and 30 by listing out the common multiples, list the multiples as shown below
| Multiples of 8 | Multiples of 30 |
| 8 | 30 |
| 16 | 60 |
| 24 | 90 |
| …. | 120 |
| 120 | 150 |
The smallest common multiple of 8 and 30 is 120.
Therefore LCM (8, 30) = 120
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Video Lesson on Applications of LCM
LCM of 8 and 30 Solved Example
The product of two numbers is 240. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 240
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 240/2
Therefore, the LCM is 120.
The probable combination for the given case is LCM(8, 30) = 120.
Frequently Asked Questions on LCM of 8 and 30
What is the LCM of 8 and 30?
List the methods used to find the LCM of 8 and 30.
What is the Relation Between GCF and LCM of 8, 30?
If the LCM of 30 and 8 is 120, Find its GCF.
Since the LCM of 30 and 8 = 120
⇒ 120 × GCF(30, 8) = 240
Therefore, the greatest common factor (GCF) = 240/120 = 2.
How to Find the LCM of 8 and 30 by Prime Factorization?
⇒ LCM of 8, 30 = 23 × 3 × 5 = 120.
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