LCM of 4, 6 and 9 is 36. The process of determining the least common multiple of 4, 6 and 9 using the common multiples can be learnt by referring to this article. The multiples of 4 are (4, 8, 12, 16, 20, ….), the multiples of 6 are (6, 12, 18, 24, 30, 36, …..) and the multiples of 9 are (9, 18, 27, 36, 45, ….) respectively. Division, Prime factorisation and listing of the multiples are the common methods used to find the LCM.
Also read: Least common multiple
What is LCM of 4, 6 and 9?
The answer to this question is 36. The LCM of 4, 6 and 9 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 6 and 9, is the smallest positive integer 36 which is divisible by both 4, 6 and 9 with no remainder.
How to Find LCM of 4, 6 and 9?
LCM of 4, 6 and 9 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4, 6 and 9 Using Prime Factorisation Method
The prime factorisation of 4, 6 and 9, respectively, is given by:
4 = 2 x 2 = 2²
6 = 2 x 3 = 2¹ x 3¹
9 = 3 x 3 = 3²
LCM (4, 6, 9) = 36
LCM of 4, 6 and 9 Using Division Method
We’ll divide the numbers (4, 6, 9) by their prime factors to get the LCM of 4, 6 and 9 using the division method (preferably common). The LCM of 4, 6 and 9 is calculated by multiplying these divisors.
|
2 |
4 |
6 |
9 |
|
2 |
2 |
3 |
9 |
|
3 |
1 |
3 |
9 |
|
3 |
1 |
1 |
3 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (4, 6, 9) = 36
LCM of 4, 6 and 9 Using Listing the Multiples
To calculate the LCM of 4, 6 and 9 by listing out the common multiples, list the multiples as shown below
|
Multiples of 4 |
Multiples of 6 |
Multiples of 9 |
|
4 |
6 |
9 |
|
8 |
12 |
18 |
|
12 |
18 |
27 |
|
16 |
24 |
36 |
|
20 |
30 |
45 |
|
24 |
36 |
54 |
|
28 |
42 |
63 |
|
32 |
48 |
72 |
|
36 |
56 |
81 |
|
40 |
60 |
90 |
LCM (4, 6, 9) = 36
Related Articles
Video Lesson on Applications of LCM
LCM of 4, 6 and 9 Solved Examples
Question: Determine the smallest number which is divisible by 4, 6 and 9 evenly.
Solution:
The smallest number which is divisible by 4, 6 and 9 exactly is the LCM.
Multiples of 4 = 4, 8, 12, 16, 20, 24,…..
Multiples of 6 = 6, 12, 18, 24, 30, 36, ….
Multiples of 9 = 9, 18, 27, 36, 45, 54, …..
Hence, the LCM is 36.
Frequently Asked Questions on LCM of 4, 6 and 9
What is the LCM of 4, 6 and 9?
If the LCM of 4, 6 and 9 is 36, determine the GCF.
LCM x GCF = 4 x 6 x 9
Given
LCM of 4, 6 and 9 is 36
36 x GCF = 216
GCF = 216/36 = 6
What are the methods used to find the LCM of 4, 6 and 9?
The methods used to find the LCM of 4, 6 and 9 are:
Division method
Prime Factorisation
Listing the multiples
In the numbers, 52, 16, 36, 20, determine the LCM of 4, 6 and 9.
Use prime factorisation to get the LCM value of 4, 6 and 9.
Using prime factorisation
4 = 2 x 2
6 = 2 x 3
9 = 3 x 3
LCM of 4, 6 and 9 is 36.
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