LCM of 45 and 54 is 270. 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. The smallest number among all common multiples of 45 and 54 is the LCM of 45 and 54. (45, 90, 135, 180, 225, 270, etc.) and (54, 108, 162, 216, 270, 324, etc.) are the first few multiples of 45 and 54, respectively.
Also read: Least common multiple
What is LCM of 45 and 54?
The answer to this question is 270. The LCM of 45 and 54 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 45 and 54, is the smallest positive integer 270 which is divisible by both 45 and 54 with no remainder.
How to Find LCM of 45 and 54?
LCM of 45 and 54 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 45 and 54 Using Prime Factorisation Method
The prime factorisation of 45 and 54, respectively, is given by:
45 = (3 × 3 × 5) = 32 × 51 and
54 = (2 × 3 × 3 × 3) = 21 × 33
LCM (45, 54) = 270
LCM of 45 and 54 Using Division Method
We’ll divide the numbers (45, 54) by their prime factors to get the LCM of 45 and 54 using the division method (preferably common). The LCM of 45 and 54 is calculated by multiplying these divisors.
| 2 | 45 | 54 |
| 3 | 45 | 27 |
| 3 | 15 | 9 |
| 3 | 5 | 3 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (45, 54) = 270
LCM of 45 and 54 Using Listing the Multiples
To calculate the LCM of 45 and 54 by listing out the common multiples, list the multiples as shown below
| Multiples of 45 | Multiples of 54 |
| 45 | 54 |
| 90 | 108 |
| 135 | 162 |
| 180 | 216 |
| 225 | 270 |
| 270 | 324 |
The smallest common multiple of 45 and 54 is 270.
Therefore LCM (45, 54) = 270
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LCM of 45 and 54 Solved Example
The product of two numbers is 2430. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 2430
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2430/9
Therefore, the LCM is 270.
The probable combination for the given case is LCM(45, 54) = 270.
Frequently Asked Questions on LCM of 45 and 54
What is the LCM of 45 and 54?
List the methods used to find the LCM of 45 and 54.
If the LCM of 54 and 45 is 270, Find its GCF.
Since the LCM of 54 and 45 = 270
⇒ 270 × GCF(54, 45) = 2430
Therefore, the greatest common factor (GCF) = 2430/270 = 9.
What is the Least Perfect Square Divisible by 45 and 54?
LCM of 45 and 54 = 2 × 3 × 3 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 45 and 54 = LCM(45, 54) × 2 × 3 × 5 = 8100 [Square root of 8100 = √8100 = ±90] Therefore, 8100 is the required number.
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