LCM of 54 and 90 is 270. LCM denotes the least common factor or multiple of any two or more given numbers. The article LCM with Examples is crafted by the faculty in simple language so that students grasp the LCM concept with ease. Students who aim to find the least common multiple of given numbers effortlessly must master the LCM concept right from the beginning itself. Let us learn the easy way of representing the least common multiple of 54 and 90 in this article.
What is LCM of 54 and 90?
The Least Common Multiple of 54 and 90 is 270.
How to Find LCM of 54 and 90?
LCM of 54 and 90 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 54 and 90 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 54 and 90 are expressed as;
54 = 2 × 3 × 3 × 3
90 = 2 × 3 × 3 × 5
LCM (54, 90) = 2 × 3 × 3 × 3 × 5 = 270
LCM of 54 and 90 Using Division Method
In the division method, to find the least common multiple of 54 and 90, we divide the numbers 54 and 90 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 54 and 90.
| 2 | 54 | 90 |
| 3 | 27 | 45 |
| 3 | 9 | 15 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (54, 90) = 2 × 3 × 3 × 3 × 5 = 270
LCM of 54 and 90 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. The below table shows the multiples of 54 and 90.
| Multiples of 54 | Multiples of 90 |
| 54 | 90 |
| 108 | 180 |
| 162 | 270 |
| 216 | 360 |
| 270 | 450 |
| 324 | 540 |
LCM (54, 90) = 270
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 90?
Solution: 270 is the smallest number that is divisible by both 54 and 90.
2. The GCD and LCM of the two numbers are 18 and 270. If one number is 54, what is the other number?
Solution: Let the other number be k
We know that,
GCD × LCM = 54 × k
k = (GCD × LCM) / 54
k = (18 × 270) / 54
k = 90
Hence the other number is 90.
Frequently Asked Questions on LCM of 54 and 90
What is the LCM of 54 and 90?
Is the LCM of 54 and 90 the same as the HCF of 54 and 90?
Name the methods used to find the LCM of 54 and 90.
The methods used to find the LCM of 54 and 90 are:
Prime Factorisation
Division method
Listing the Multiples
Find the LCM of 54 and 90 using the prime factorisation method.
In prime factorisation, to find the LCM, we express the numbers as the product of prime factors
54 = 2 × 3 × 3 × 3
90 = 2 × 3 × 3 × 5
LCM (54, 90) = 2 × 3 × 3 × 3 × 5 = 270
What is the GCF if the LCM of 54 and 90 is 270?
GCF × LCM = 54 × 90
Given
LCM = 270
GCF × 270 = 54 × 90
GCF = 18
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