LCM of 12, 15, 18 and 27 is 540. For a stronghold on the methods of finding the LCM of 12, 15, 18 and 27, this article is of great help for the students. The least common multiple of 12, 15, 18 and 27 is the number which is the smallest and evenly divisible by the given numbers. The multiples of 12 are (12, 24, 36, 48, 60, ….), the multiples of 15 are (15, 30, 45, 60, 75, ….), the multiples of 18 are (18, 36, 54, 72, 90, …..) and the multiples of 27 are (27, 54, 81, 108, 135, ….) respectively. Division, Prime factorisation and listing of the multiples are the common methods we can make use of to determine the LCM value.
Also read: Least common multiple
What is LCM of 12, 15, 18 and 27?
The answer to this question is 540. The LCM of 12, 15, 18 and 27 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12, 15, 18 and 27, is the smallest positive integer 540 which is divisible by both 12, 15, 18 and 27 with no remainder.
How to Find LCM of 12, 15, 18 and 27?
LCM of 12, 15, 18 and 27 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 15, 18 and 27 Using Prime Factorisation Method
The prime factorisation of 12, 15, 18 and 27, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
15 = 3 x 5 = 3¹ x 5¹
18 = 2 x 3 x 3 = 2¹ x 3²
27 = 3 x 3 x 3 = 3³
LCM (12, 15, 18, 27) = 540
LCM of 12, 15, 18 and 27 Using Division Method
We’ll divide the numbers (12, 15, 18, 27) by their prime factors to get the LCM of 12, 15, 18 and 27 using the division method (preferably common). The LCM of 12, 15, 18 and 27 is calculated by multiplying these divisors.
|
2 |
12 |
15 |
18 |
27 |
|
2 |
6 |
15 |
9 |
27 |
|
3 |
3 |
15 |
9 |
27 |
|
3 |
1 |
5 |
3 |
9 |
|
3 |
1 |
5 |
1 |
3 |
|
5 |
1 |
5 |
1 |
1 |
|
x |
1 |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (12, 15, 18, 27) = 540
LCM of 12, 15, 18 and 27 Using Listing the Multiples
To calculate the LCM of 12, 15, 18 and 27 by listing out the common multiples, list the multiples as shown below
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 504, 516, 528, 540, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 480, 495, 510, 525, 540, . . . .
Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, . . . ., 468, 486, 504, 522, 540, . . .
Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, . . . ., 432, 459, 486, 513, 540, . . . .
LCM (12, 15, 18, 27) = 540
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LCM of 12, 15, 18 and 27 Solved Examples
Question: From the numbers 24, 30, 27 and 540, find the LCM of 12, 15, 18 and 27.
Solution:
We know that
LCM of 12, 15, 18 and 27 is the smallest common multiple of 12, 15, 18 and 27.
The number 540 satisfies this condition.
Hence, the LCM is 540.
Frequently Asked Questions on LCM of 12, 15, 18 and 27
What is the LCM of 12, 15, 18 and 27?
If the LCM of 12, 15, 18 and 27 is 540, find the GCF.
LCM x GCF = 12 x 15 x 18 x 27
Given
LCM of 12, 15, 18 and 27 is 540
540 x GCF = 87480
GCF = 87480/540 = 162
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