LCM of 12 and 30 is 60. The LCM is the multiple which is divisible by the two given numbers evenly. We can obtain the least common multiple of 12 and 30 by considering the smallest common multiples. (12, 24, 36, 48, ….) are the multiples of 12 and (30, 60, 90, 120, 150, ….) are the multiples of 30 respectively. Prime factorisation, division and listing of the multiples are the methods used to determine the LCM.
Also read: Least common multiple
What is LCM of 12 and 30?
The answer to this question is 60. The LCM of 12 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 30, is the smallest positive integer 60 which is divisible by both 12 and 30 with no remainder.
How to Find LCM of 12 and 30?
LCM of 12 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 30 Using Prime Factorisation Method
The prime factorisation of 12 and 30, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
LCM (12, 30) = 60
LCM of 12 and 30 Using Division Method
We’ll divide the numbers (12, 30) by their prime factors to get the LCM of 12 and 30 using the division method (preferably common). The LCM of 12 and 30 is calculated by multiplying these divisors.
| 2 | 12 | 30 |
| 2 | 6 | 15 |
| 3 | 3 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 30) = 60
LCM of 12 and 30 Using Listing the Multiples
To calculate the LCM of 12 and 30 by listing out the common multiples, list the multiples as shown below.
| Multiples of 12 | Multiples of 30 |
| 12 | 30 |
| 24 | 60 |
| 36 | 90 |
| 48 | 120 |
| 60 | 150 |
| 72 | 180 |
LCM (12, 30) = 60
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Video Lesson on Applications of LCM
LCM of 12 and 30 Solved Example
Question: The product of two numbers is 360. If the GCF is 6, find the LCM.
Solution:
Given
GCF = 6
Product of two numbers = 360
We know that
LCM x GCD = product of two numbers
LCM x 6 = 360
LCM = 360/6 = 60
Therefore, the LCM is 60.
Frequently Asked Questions on LCM of 12 and 30
What is the LCM of 12 and 30?
What is the GCF if the LCM of 12 and 30 is 60?
LCM x GCF = 12 x 30
Given,
LCM of 12 and 30 is 60
60 x GCF = 360
GCF = 360/60 = 60
List the methods used to find the LCM of 12 and 30.
The methods used to find the LCM of 12 and 30 are;
Prime Factorisation
Division method
Listing the multiples
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