LCM of 54 and 72 is 216. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. Students can easily solve any problem based on the LCM concept by referring to the article Least Common Multiple (LCM). This article is framed by the experts in simple language to help students get a proper grasp of the LCM concept. Let us have a look at how to find the least common multiple of 54 and 72 in a simple method in this article.
What is LCM of 54 and 72?
The Least Common Multiple of 54 and 72 is 216.
How to Find LCM of 54 and 72?
The LCM of 54 and 72 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 54 and 72 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 72 can be expressed as;
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
LCM (54, 72) = 2 × 2 × 2 × 3 × 3 × 3 = 216
LCM of 54 and 72 Using Division Method
In the division method, we divide the numbers 54 and 72 by a common prime number until the remainder is a prime number or one. The product of these divisors represents the least common multiple of 54 and 72.
| 2 | 54 | 72 |
| 2 | 27 | 36 |
| 2 | 27 | 18 |
| 3 | 27 | 9 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (54, 72) = 2 × 2 × 2 × 3 × 3 × 3 = 216
LCM of 54 and 72 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The below table shows the multiples of 54 and 72.
| Multiples of 54 | Multiples of 72 |
| 54 | 72 |
| 108 | 144 |
| 162 | 216 |
| 216 | 288 |
| 270 | 360 |
LCM (54, 72) = 216
Related Articles
Prime Factorisation 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 72?
Solution: 216 is the smallest number that is divisible by both 54 and 72.
2. What is the lowest common factor of 54 and 72?
Solution: The lowest common factor of 54 and 72 is 216.
Frequently Asked Questions on LCM of 54 and 72
What is the LCM of 54 and 72?
Is the LCM of 54 and 72 the same as the HCF of 54 and 72?
List the first five multiples of 54 and 72.
The first five multiples of 54 and 72 are:
Multiples of 54 = 54, 108, 162, 216, and 270
Multiples of 72 = 72, 144, 216, 288, and 360
Find the GCF if the LCM of 54 and 72 is 216.
GCF × LCM = 54 × 72
Given
LCM = 216
GCF × 216 = 54 × 72
GCF = 18
List the methods to determine the LCM of 54 and 72.
The methods used to determine the LCM of 54 and 72 are
Prime Factorisation
Division Method
Listing the Multiples
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