LCM of 12 and 27 is 108. The number divisible by the given two numbers exactly provides the LCM value. Among the common multiples, the least common multiple of 12 and 27 can be calculated. The multiples of 12 are (12, 24, 36, 48, 60, 72, 84, ….) and the multiples of 27 are (27, 54, 81, 108, 135, ….) respectively. The methods to calculate the LCM value of the numbers given are prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 12 and 27?
The answer to this question is 108. The LCM of 12 and 27 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 27, is the smallest positive integer 108 which is divisible by both 12 and 27 with no remainder.
How to Find LCM of 12 and 27?
LCM of 12 and 27 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 27 Using Prime Factorisation Method
The prime factorisation of 12 and 27, respectively, is given by:
12 = 2 x 2 x 3 = 2² x 3¹
27 = 3 x 3 x 3 = 3³
LCM (12, 27) = 108
LCM of 12 and 27 Using Division Method
We’ll divide the numbers (12, 27) by their prime factors to get the LCM of 12 and 27 using the division method (preferably common). The LCM of 12 and 27 is calculated by multiplying these divisors.
2 | 12 | 27 |
2 | 6 | 27 |
3 | 3 | 27 |
3 | 1 | 9 |
3 | 1 | 3 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 27) = 108
LCM of 12 and 27 Using Listing the Multiples
To calculate the LCM of 12 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, …..
Multiples of 27 = 27, 54, 81, 108, 135, ……
LCM (12, 27) = 108
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LCM of 12 and 27 Solved Examples
Question: The LCM and GCD of two numbers are 108 and 3 respectively. If one number is 27, what is the other number?
Solution:
Consider the number as z.
We know that
GCD x LCM = 27 x z
z = (GCD x LCM)/27
Substituting the values
z = (3 x 108)/27
z = 12
Hence, the other number is 12.
Frequently Asked Questions on LCM of 12 and 27
Q1
If the LCM of 12 and 27 is 108, what is its GCF?
We know that
LCM x GCF = 12 x 27
As LCM (12, 27) is 108
108 x GCF = 324
GCF = 324/108 = 3
Q2
Find the LCM of 12 and 27.
To find the LCM, we first should understand the multiples of 12 and 27. The smallest multiple exactly divisible by 12 and 27 is 108.
Q3
Show the relation between GCF and LCM of 12 and 27.
The relation between GCF and LCM of 12 and 27 is
LCM x GCF = 12 x 27
LCM x GCF = 324
Q4
What is the LCM of 12 and 27?
The LCM of 12 and 27 is 108.
Q5
What methods can we use to get the LCM of 12 and 27?
The methods we can use to get the LCM of 12 and 27 are division, listing multiples and prime factorisation.
