LCM of 9, 12 and 18 is 36. The smallest number evenly divisible from the multiples of the 9, 12 and 18 gives the LCM value. By going through the common multiples list, the least common multiple of 9, 12 and 18 can be found. (9, 18, 27, 36, 45, ….), (12, 24, 36, 48, 60, …..) and (18, 36, 54, 72, 90,….) are the multiples of 9, 12 and 18. Students can obtain the value of LCM using the prime factorisation method, division method and listing the multiples.
Also read: Least common multiple
What is LCM of 9, 12 and 18?
The answer to this question is 36. The LCM of 9, 12 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9, 12 and 18, is the smallest positive integer 36 which is divisible by both 9, 12 and 18 with no remainder.
How to Find LCM of 9, 12 and 18?
LCM of 9, 12 and 18 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9, 12 and 18 Using Prime Factorisation Method
The prime factorisation of 9, 12 and 18, respectively, is given by:
9 = 3 × 3 = 3²
12 = 2 × 2 × 3 = 2²× 3¹
18 = 2 × 3 × 3 = 2¹ × 3²
LCM (9, 12, 18) = 36
LCM of 9, 12 and 18 Using Division Method
We’ll divide the numbers (9, 12, 18) by their prime factors to get the LCM of 9, 12 and 18 using the division method (preferably common). The LCM of 9, 12 and 18 is calculated by multiplying these divisors.
|
2 |
9 |
12 |
18 |
|
2 |
9 |
6 |
9 |
|
3 |
9 |
3 |
9 |
|
3 |
3 |
1 |
3 |
|
× |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (9, 12, 18) = 36
LCM of 9, 12 and 18 Using Listing the Multiples
To calculate the LCM of 9, 12 and 18 by listing out the common multiples, list the multiples as shown below
|
Multiples of 9 |
Multiples of 12 |
Multiples of 18 |
|
9 |
12 |
18 |
|
18 |
24 |
36 |
|
27 |
36 |
54 |
|
36 |
48 |
72 |
|
45 |
60 |
90 |
|
54 |
72 |
108 |
LCM (9, 12, 18) = 36
Related Articles
Video Lesson on Applications of LCM
LCM of 9, 12 and 18 Solved Examples
Question: What is the smallest number divisible exactly by 9, 12 and 18?
Solution:
The smallest number divisible exactly by 9, 12 and 18 is the value of the LCM.
Multiples of 9 = 9, 18, 27, 36, 45, 54, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, 72, . . . .
Multiples of 18 = 18, 36, 54, 72, 90, 108, . . . .
Hence, the LCM is 36.
Frequently Asked Questions on LCM of 9, 12 and 18
What is the LCM of 9, 12 and 18?
The LCM of 9, 12 and 18 is 36.
The smallest multiple exactly divisible by 9, 12 and 18 should be found.
From the multiples of the given numbers, the smallest common multiple exactly divisible by 9, 12 and 18 is 36.
List the methods which can be used to get the LCM value of 9, 12 and 18.
Find GCF if the LCM of 9, 12 and 18 is 36.
LCM × GCF = 9 × 12 × 18
Given
LCM of 9, 12 and 18 = 36
36 × GCF = 1944
GCF = 1944/36 = 54
Among 36, 96, 110 and 11, find the LCM of 9, 12 and 18.
Using prime factorisation, find the LCM of 9, 12 and 18.
Using prime factorisation,
9 = 3 × 3
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM of 9, 12 and 18 is 36.
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