LCM of 54 and 12 is 108. LCM denotes the smallest positive number which is a multiple of two or more numbers. The article LCM with Examples can be used as the best study material by the students to get a strong grip on the LCM concept. Solving the problems with the help of the article designed by experts mainly improves problem-solving and time management skills, which are essential from an exam perspective. Here, we will discuss how to find the least common multiple of 54 and 12 using a simple process.
What is LCM of 54 and 12?
The answer to this question is 108.
How to Find LCM of 54 and 12?
LCM of 54 and 12 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 54 and 12 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 54 and 12 can be expressed as;
54 = 2 × 3 × 3 × 3
12 = 2 × 2 × 3
LCM (54, 12) = 2 × 2 × 3 × 3 × 3 = 108
LCM of 54 and 12 Using Division Method
In this method, we divide the numbers 54 and 12 by a common prime number until the remainder is a prime number or one. The product of these divisors gives the least common multiple of 54 and 12.
| 2 | 54 | 12 |
| 2 | 27 | 6 |
| 3 | 27 | 3 |
| 3 | 9 | 1 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (54, 12) = 2 × 2 × 3 × 3 × 3 = 108
LCM of 54 and 12 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 54 and 12.
| Multiples of 54 | Multiples of 12 |
| 54 | 12 |
| 108 | 24 |
| 162 | 36 |
| 216 | 48 |
| 270 | 60 |
| 324 | 72 |
| 378 | 84 |
| 432 | 96 |
| 486 | 108 |
| 540 | 120 |
LCM (54, 12) = 108
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 54 and 12?
Solution: 108 is the smallest number that is divisible by both 54 and 12.
2. The GCD and LCM of the two numbers are 6 and 108. If one number is 54. What is the other number?
Solution: Let the other number be r
We know that
GCF × LCM = 54 × r
r = (GCF × LCM) / 54
r = (6 × 108) / 54
r = 12
Therefore the other number is 12.
Frequently Asked Questions on LCM of 54 and 12
What is the LCM of 54 and 12?
Is the LCM of 54 and 12 and the HCF of 54 and 12 are same?
Name the methods used to find the LCM of 54 and 12.
The methods used to find the LCM of 54 and 12 are as follows:
Prime Factorisation
Division method
Listing the Multiples
Calculate the GCF if the LCM of 54 and 12 is 108.
GCF × LCM
Given
LCM = 108
GCF × 108 = 54 × 12
GCF = 6
Comments