LCM of 28 and 30 is 420. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 28 and 30, the LCM of 28 and 30 is the smallest number. (28, 56, 84, 112, 140,…) and (30, 60, 90, 120, 150,…) are the first few multiples of 28 and 30. Prime factorization, division, and listing multiples are the three most frequent methods for calculating the LCM of 28 and 30.
Also read: Least common multiple
What is LCM of 28 and 30?
The answer to this question is 420. The LCM of 28 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 28 and 30, is the smallest positive integer 420 which is divisible by both 28 and 30 with no remainder.
How to Find LCM of 28 and 30?
LCM of 28 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 28 and 30 Using Prime Factorisation Method
The prime factorisation of 28 and 30, respectively, is given by:
28 = (2 × 2 × 7) = 22 × 71 and
30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (28, 30) = 420
LCM of 28 and 30 Using Division Method
We’ll divide the numbers (28, 30) by their prime factors to get the LCM of 28 and 30 using the division method (preferably common). The LCM of 28 and 30 is calculated by multiplying these divisors.
| 2 | 28 | 30 |
| 2 | 14 | 15 |
| 3 | 7 | 15 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (28, 30) = 420
LCM of 28 and 30 Using Listing the Multiples
To calculate the LCM of 28 and 30 by listing out the common multiples, list the multiples as shown below
| Multiples of 28 | Multiples of 30 |
| 28 | 30 |
| 56 | 60 |
| 84 | 90 |
| ….. | ….. |
| 420 | 420 |
The smallest common multiple of 28 and 30 is 420.
Therefore LCM (28, 30) = 420
Related Articles
Video Lesson on Applications of LCM
LCM of 28 and 30 Solved Example
Question: The product of two numbers is 840. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 840
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 840/2
Therefore, the LCM is 420.
The probable combination for the given case is LCM(28, 30) = 420.
Frequently Asked Questions on LCM of 28 and 30
What is the LCM of 28 and 30?
List the methods used to find the LCM of 28 and 30.
If the LCM of 30 and 28 is 420, Find its GCF.
Since the LCM of 30 and 28 = 420
⇒ 420 × GCF(30, 28) = 840
Therefore, the greatest common factor (GCF) = 840/420 = 2.
What is the Relation Between GCF and LCM of 28, 30?
How to Find the LCM of 28 and 30 by Prime Factorization?
⇒ LCM of 28, 30 = 22 × 71 × 21 × 31 × 51= 420.
Comments