LCM of 3, 4 and 12 is 12. The number divisible evenly by 3, 4 and 12 is the LCM value. Least common multiples of 3, 4 and 12 is the common multiple of the given numbers. (3, 6, 9, 12, 15, 18, ….), (4, 8, 12, 16, 20, …..) and (12, 24, 36, 48, 60,….) are the multiples of 3, 4 and 12. The LCM of two numbers considering the prime factorization method, division method and listing out the multiples is given accurately in this article.
Also read: Least common multiple
What is LCM of 3, 4 and 12?
The answer to this question is 12. The LCM of 3, 4 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3, 4 and 12, is the smallest positive integer 12 which is divisible by both 3, 4 and 12 with no remainder.
How to Find LCM of 3, 4 and 12?
LCM of 3, 4 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 4 and 12 Using Prime Factorisation Method
The prime factorisation of 3, 4 and 12, respectively, is given by:
3 = 3 = 3¹
4 = 2 x 2 = 2²
12 = 2 x 2 x 3 = 2² x 3¹
LCM (3, 4, 12) = 12
LCM of 3, 4 and 12 Using Division Method
We’ll divide the numbers (3, 4, 12) by their prime factors to get the LCM of 3, 4 and 12 using the division method (preferably common). The LCM of 3, 4 and 12 is calculated by multiplying these divisors.
|
2 |
3 |
4 |
12 |
|
2 |
3 |
2 |
6 |
|
3 |
3 |
1 |
3 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (3, 4, 12) = 12
LCM of 3, 4 and 12 Using Listing the Multiples
To calculate the LCM of 3, 4 and 12 by listing out the common multiples, list the multiples as shown below
|
Multiples of 3 |
Multiples of 4 |
Multiples of 12 |
|
3 |
4 |
12 |
|
6 |
8 |
24 |
|
9 |
12 |
36 |
|
12 |
16 |
48 |
|
15 |
20 |
60 |
|
18 |
24 |
72 |
|
21 |
28 |
84 |
LCM (3, 4, 12) = 12
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 3, 4 and 12 Solved Examples
Question: What is the smallest number divisible evenly by 3, 4 and 12?
Solution:
We know that
The smallest number which is exactly divisible by 3, 4 and 12 is the LCM.
Multiples of 3 = 3, 6, 9, 12, 15, 18, …..
Multiples of 4 = 4, 8, 12, 16, 20, …..
Multiples of 12 = 12, 24, 36, 48, 60, …..
Hence, the LCM of 3, 4 and 12 is 12.
Frequently Asked Questions on LCM of 3, 4 and 12
Calculate the LCM of 3, 4 and 12 with the help of the prime factorization method.
To determine the LCM using the prime factorization, we first should know the prime factors.
3 = 3 = 3¹
4 = 2 x 2 = 2²
12 = 2 x 2 x 3 = 2² x 3¹
LCM of 3, 4 and 12 is the product of prime factors raised to the highest exponent among the numbers 3, 4 and 12
LCM of 3, 4 and 12 = 12
If the LCM of 3, 4 and 12 is 12, find the GCF.
LCM x GCF = 3 x 4 x 12
Given
LCM of 3, 4 and 12 = 12
12 x GCF = 144
GCF = 144/12 = 12
Write the relation between GCF and LCM of 3, 4 and 12.
The relation between GCF and LCM of 3, 4 and 12 is
LCM x GCF = 3 x 4 x 12
LCM x GCF = 144
The GCD is 12 and the product of two numbers is 144. Find the LCM of 3, 4 and 12.
Given
GCD = 12
Product = 144
LCM x GCD = Product
LCM = Product/GCD = 144/12 = 12
Hence, the LCM of 3, 4 and 12 is 12.
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