LCM of 6, 12 and 18 is 36. The number which evenly divides 6, 12 and 18 gives the value of LCM. The common multiples of the two numbers will provide the least common multiple of 6, 12 and 18. The multiples of 6 are (6, 12, 18, 24, 30, 36, ….), the multiples of 12 are (12, 24, 36, 48, 60, …..) and the multiples of 18 are (18, 36, 54, 72, 90, …..) respectively. For a clear-cut knowledge of the LCM concept and methods like prime factorisation, division and listing out the multiples, make use of the reference materials at BYJU’S.
Also read: Least common multiple
What is LCM of 6, 12 and 18?
The answer to this question is 36. The LCM of 6, 12 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 6, 12 and 18, is the smallest positive integer 36 which is divisible by both 6, 12 and 18 with no remainder.
How to Find LCM of 6, 12 and 18?
LCM of 6, 12 and 18 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 12 and 18 Using Prime Factorisation Method
The prime factorisation of 6, 12 and 18, respectively, is given by:
6 = 2 x 3 = 2¹ x 3¹
12 = 2 x 2 x 3 = 2² x 3¹
18 = 2 x 3 x 3 = 2¹ x 3²
LCM (6, 12, 18) = 36
LCM of 6, 12 and 18 Using Division Method
We’ll divide the numbers (6, 12, 18) by their prime factors to get the LCM of 6, 12 and 18 using the division method (preferably common). The LCM of 6, 12 and 18 is calculated by multiplying these divisors.
|
2 |
6 |
12 |
18 |
|
2 |
3 |
6 |
9 |
|
3 |
3 |
3 |
9 |
|
3 |
1 |
1 |
3 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (6, 12, 18) = 36
LCM of 6, 12 and 18 Using Listing the Multiples
To calculate the LCM of 6, 12 and 18 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 6 |
Multiples of 12 |
Multiples of 18 |
|
6 |
12 |
18 |
|
12 |
24 |
36 |
|
18 |
36 |
54 |
|
24 |
48 |
72 |
|
30 |
60 |
90 |
|
36 |
72 |
108 |
|
42 |
84 |
126 |
LCM (6, 12, 18) = 36
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LCM of 6, 12 and 18 Solved Examples
Question: Determine the smallest number divisible by 6, 12 and 18 exactly.
Solution:
The smallest number divisible by 6, 12 and 18 exactly is LCM.
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, ….
Multiples of 12 = 12, 24, 36, 48, 60, 72, ….
Multiples of 18 = 18, 36, 54, 72, 90, 108, …..
Therefore, the LCM of 6, 12 and 18 is 36.
Frequently Asked Questions on LCM of 6, 12 and 18
Find the GCF if the LCM of 6, 12 and 18 is 36.
We know that,
LCM x GCF = 6 x 12 x 18
As LCM (6, 12, 18) is 36
36 x GCF = 1296
GCF = 1296/36 = 36
Find the LCM of 6, 12 and 18.
Show the relation between GCF and LCM of 6, 12 and 18.
The relation between GCF and LCM of 6, 12 and 18 is
LCM x GCF = 6 x 12 x 18
LCM x GCF = 1296
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