LCM of 3 and 12 is 12. The smallest number among all common multiples of 3 and 12 is the LCM of 3 and 12. (3, 6, 9, 12, 15, 18, 21, etc.) and (12, 24, 36, 48, 60, etc.) are the first few multiples of 3 and 12. In mathematics, the LCM of Two Numbers is the value that is evenly divisible by the two values. To find the LCM of 3 and 12, there are three typical methods: prime factorization, listing multiples, and division.
What is LCM of 3 and 12?
The answer to this question is 12. The LCM of 3 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 12, is the smallest positive integer 12 which is divisible by both 3 and 12 with no remainder.
Also read: Least common multiple
How to Find LCM of 3 and 12?
LCM of 3 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 12 Using Prime Factorisation Method
The prime factorisation of 3 and 12, respectively, is given by:
(3) = 31
and
12 = (2 × 2 × 3) = 22 × 31
LCM (3, 12) = 12
LCM of 3 and 12 Using Division Method
We’ll divide the numbers (3, 12) by their prime factors to get the LCM of 3 and 12 using the division method (preferably common). The LCM of 3 and 12 is calculated by multiplying these divisors.
| 2 | 3 | 12 |
| 2 | 3 | 6 |
| 3 | 3 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (3, 12) = 12.
LCM of 3 and 12 Using Listing the Multiples
To calculate the LCM of 3 and 12 by listing out the common multiples, list the multiples as shown below.
| Multiples of 3 | Multiples of 12 |
| 3 | 12 |
| 6 | 24 |
| 9 | 36 |
| 12 | 48 |
| 15 | 60 |
The smallest common multiple of 3 and 12 is 12.
LCM (3, 12) = 12
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LCM of 3 and 12 Solved Example
The product of two numbers is 36. If their GCD is 3, what is their LCM?
Given: GCD = 3
product of numbers = 36
LCM × GCD = product of numbers
LCM = Product/GCD = 36/3
Therefore, the LCM is 12.
The probable combination for the given case is LCM(3, 12) = 12.
Frequently Asked Questions on LCM of 3 and 12
What is the LCM of 3 and 12?
List the methods used to find the LCM of 3 and 12.
If the LCM of 12 and 3 is 12, Find its GCF.
Since the LCM of 12 and 3 = 12
⇒ 12 × GCF(12, 3) = 36
Therefore, the greatest common factor (GCF) = 36/12 = 3.C
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