LCM of 4 and 12 is 12. In mathematics, the LCM of any two numbers is the value that is evenly divisible by the two values. LCM of 4 and 12 is the smallest number among all common multiples of 4 and 12. The first few multiples of 4 and 12 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (12, 24, 36, 48, 60, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 12 – by listing multiples, by division method, and by prime factorization.
Also read: Least common multiple
What is LCM of 4 and 12?
The answer to this question is 12. The LCM of 4 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4 and 12, is the smallest positive integer 12 which is divisible by both 4 and 12 with no remainder.
How to Find LCM of 4 and 12?
LCM of 4 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4 and 12 Using Prime Factorisation Method
The prime factorisation of 4 and 12, respectively, is given by:
4 = (2 × 2) = 22 and
12 = (2 × 2 × 3) = 22 × 31
LCM (4, 12) = 12
LCM of 4 and 12 Using Division Method
We’ll divide the numbers (4, 12) by their prime factors to get the LCM of 4 and 12 using the division method (preferably common). The LCM of 4 and 12 is calculated by multiplying these divisors.
|
2 |
4 |
12 |
|
2 |
2 |
6 |
|
3 |
1 |
3 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (4, 12) = 12
LCM of 4 and 12 Using Listing the Multiples
To calculate the LCM of 4 and 12 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 4 |
Multiples of 12 |
|
4 |
12 |
|
8 |
24 |
|
12 |
36 |
|
16 |
48 |
|
20 |
60 |
The smallest common multiple of 4 and 12 is 12.
LCM (4, 12) = 12
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LCM of 4 and 12 Solved Example
The product of two numbers is 48. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 48
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 48/4
Therefore, the LCM is 12.
The probable combination for the given case is LCM(4, 12) = 12.
Frequently Asked Questions on LCM of 4 and 12
What is the LCM of 4 and 12?
List the methods used to find the LCM of 4 and 12.
If the LCM of 12 and 4 is 12, Find its GCF..
Since the LCM of 12 and 4 = 12
⇒ 12 × GCF(12, 4) = 48
Therefore, the GCF (greatest common factor) = 48/12 = 4.
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