LCM of 12 and 15 is 60. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all frequent multiples of 12 and 15 is the LCM of 12 and 15. (12, 24, 36, 48, 60, 72, 84, etc.) and (15, 30, 45, 60, etc.) are the first few multiples of 12 and 15, respectively. There are three typical ways for calculating the LCM of 12 and 15: division, prime factorization, and listing multiples.
Also read: Least common multiple
What is LCM of 12 and 15?
The answer to this question is 60. The LCM of 12 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 15, is the smallest positive integer 60 which is divisible by both 12 and 15 with no remainder.
How to Find LCM of 12 and 15?
LCM of 12 and 15 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 15 Using Prime Factorisation Method
The prime factorisation of 12 and 15, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3
15 = 3 x 5
LCM (12, 15) = 60
LCM of 12 and 15 Using Division Method
We’ll divide the numbers (12, 15) by their prime factors to get the LCM of 12 and 15 using the division method (preferably common). The LCM of 12 and 15 is calculated by multiplying these divisors.
| 2 | 12 | 15 |
| 2 | 6 | 15 |
| 3 | 3 | 15 |
| 5 | 1 | 5 |
| 1 | 1 |
No further division can be done.Â
Hence, LCM (12, 15) = 60
LCM of 12 and 15 Using Listing the Multiples
To calculate the LCM of 12 and 15 by listing out the common multiples, list the multiples as shown belowÂ
| Multiples of 12 | Multiples of 15 |
| 12 | 15 |
| 24 | 30 |
| 36 | 45 |
| 48 | 60 |
| 60 | 75 |
The smallest common multiple of 12 and 15 is 60.
LCM (12, 15) = 60
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Video Lesson on Applications of LCM
LCM of 12 and 15 Solved ExampleÂ
The product of two numbers is 180. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 180
Because LCM × GCD = product of numbers
Which implies LCM = Product/GCD = 180/3
Therefore, the LCM is 60.
The probable combination for the given case is LCM(12, 15) = 60.
Frequently Asked Questions on LCM of 12 and 15
What is the LCM of 12 and 15?
List the methods used to find the LCM of 12 and 15.
If the LCM of 15 and 12 is 60, Find its GCF.
Since the LCM of 15 and 12 = 60
⇒ 60 × GCF(15, 12) = 180
Therefore, the greatest common factor = 180/60 = 3.
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