LCM of 54 and 27 is 54. LCM of 54 and 27 is the smallest number among all common multiples of 54 and 27. The first few multiples of 54 and 27 are (54, 108, 162, 216, 270, . . . ) and (27, 54, 81, 108, 135, 162, 189, . . . ) respectively. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 54 and 27?
The answer to this question is 54. The LCM of 54 and 27 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 54 and 27, is the smallest positive integer 54 which is divisible by both 54 and 27 with no remainder.
How to Find LCM of 54 and 27?
LCM of 54 and 27 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 54 and 27 Using Prime Factorisation Method
The prime factorisation of 54 and 27, respectively, is given by:
54 = (2 × 3 × 3 × 3) = 21 × 33 and
27 = (3 × 3 × 3) = 33
LCM (54, 27) = 54
LCM of 54 and 27 Using Division Method
We’ll divide the numbers (54, 27) by their prime factors to get the LCM of 54 and 27 using the division method (preferably common). The LCM of 54 and 27 is calculated by multiplying these divisors.
| 2 | 54 | 27 |
| 3 | 27 | 27 |
| 3 | 9 | 9 |
| 3 | 3 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (54, 27) = 54
LCM of 54 and 27 Using Listing the Multiples
To calculate the LCM of 54 and 27 by listing out the common multiples, list the multiples as shown below.
| Multiples of 54 | Multiples of 27 |
| 54 | 27 |
| 108 | 54 |
| 162 | 81 |
| 216 | 108 |
| 270 | 135 |
The smallest common multiple of 54 and 27 is 54.
Therefore LCM (54, 27) = 72
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LCM of 54 and 27 Solved Example
The product of two numbers is 1458. If their GCD is 27, what is their LCM?
Solution:
Given: GCD = 27
product of numbers = 1458
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1458/27
Therefore, the LCM is 54.
The probable combination for the given case is LCM(54, 27) = 54.
Frequently Asked Questions on LCM of 54 and 27
What is the LCM of 54 and 27?
List the methods used to find the LCM of 54 and 27.
If the LCM of 27 and 54 is 54, Find its GCF.
Since the LCM of 27 and 54 = 54
⇒ 54 × GCF(27, 54) = 1458
Therefore, the GCF = 1458/54 = 27.
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