LCM of 4, 9 and 12 is 36. The value evenly divisible by 4, 9 and 12 is the LCM. The least common multiple of 4, 9 and 12 can be calculated with the help of the common multiples. The multiples of 4 are (4, 8, 12, 16, 20, 24, ….), the multiples of 9 are (9, 18, 27, 36, 45, …..) and the multiples of 12 are (12, 24, 36, 48, 60, ….) respectively. Prime factorisation, listing of the multiples and division are the most commonly used methods to find the LCM.
Also read: Least common multiple
What is LCM of 4, 9 and 12?
The answer to this question is 36. The LCM of 4, 9 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 9 and 12, is the smallest positive integer 36 which is divisible by both 4, 9 and 12 with no remainder.
How to Find LCM of 4, 9 and 12?
LCM of 4, 9 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4, 9 and 12 Using Prime Factorisation Method
The prime factorisation of 4, 9 and 12, respectively, is given by:
4 = 2 x 2 = 2²
9 = 3 x 3 = 3²
12 = 2 x 2 x 3 = 2² x 3¹
LCM (4, 9, 12) = 36
LCM of 4, 9 and 12 Using Division Method
We’ll divide the numbers (4, 9, 12) by their prime factors to get the LCM of 4, 9 and 12 using the division method (preferably common). The LCM of 4, 9 and 12 is calculated by multiplying these divisors.
|
2 |
4 |
9 |
12 |
|
2 |
2 |
9 |
6 |
|
3 |
1 |
9 |
3 |
|
3 |
1 |
3 |
1 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (4, 9, 12) = 36
LCM of 4, 9 and 12 Using Listing the Multiples
To calculate the LCM of 4, 9 and 12 by listing out the common multiples, list the multiples as shown below
|
Multiples of 4 |
Multiples of 9 |
Multiples of 12 |
|
4 |
9 |
12 |
|
8 |
18 |
24 |
|
12 |
27 |
36 |
|
16 |
36 |
48 |
|
20 |
45 |
60 |
|
24 |
54 |
72 |
|
28 |
63 |
84 |
|
32 |
72 |
96 |
|
36 |
81 |
108 |
|
40 |
90 |
120 |
LCM (4, 9, 12) = 36
Related Articles
Video Lesson on Applications of LCM
LCM of 4, 9 and 12 Solved Examples
Question: Calculate the smallest number which is exactly divisible by 4, 9 and 12.
Solution:
The smallest number divisible by 4, 9 and 12 exactly is the LCM
(4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ….) are the multiples of 4
(9, 18, 27, 36, 45, 54, 63, ….) are the multiples of 9
(12, 24, 36, 48, 60, …..) are the multiples of 12
Hence, LCM of 4, 9 and 12 is 36.
Frequently Asked Questions on LCM of 4, 9 and 12
What is the LCM of 4, 9 and 12?
What is the GCF if the LCM of 4, 9 and 12 is 36?
LCM x GCF = 4 x 9 x 12
Given,
LCM of 4, 9 and 12 is 36
36 x GCF = 432
GCF = 432/36 = 12
What are the methods which can be applied to find the LCM of 4, 9 and 12?
The product of three numbers is 432 and the GCD is 12. Find the LCM.
Given
Product of two numbers = 432
GCD = 12
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 432/12 = 36
Therefore, the LCM is 36.
Using prime factorisation, find the LCM of 4, 9 and 12.
Using prime factorisation
4 = 2 x 2
9 = 3 x 3
12 = 2 x 2 x 3
LCM of 4, 9 and 12 is 36.
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