LCM of 18 and 45 is 90. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 18 and 45 is the LCM of 18 and 45. (18, 36, 54, 72, 90, 108, 126, etc.) and (45, 90, 135, 180, 225, 270, etc.) are the first few multiples of 18 and 45, respectively. There are three typical ways for calculating the LCM of 18 and 45: listing multiples, prime factorization, and division. .
Also read: Least common multiple
What is LCM of 18 and 45?
The answer to this question is 90. The LCM of 18 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 45, is the smallest positive integer 90 which is divisible by both 18 and 45 with no remainder.
How to Find LCM of 18 and 45?
LCM of 18 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 45 Using Prime Factorisation Method
The prime factorisation of 18 and 45, respectively, is given by:
18 = (2 × 3 × 3) = 21 × 32 and
45 = (3 × 3 × 5) = 32 × 51
LCM (18, 45) = 90
LCM of 18 and 45 Using Division Method
We’ll divide the numbers (18, 45) by their prime factors to get the LCM of 18 and 45 using the division method (preferably common). The LCM of 18 and 45 is calculated by multiplying these divisors.
| 2 | 18 | 45 |
| 3 | 9 | 45 |
| 3 | 3 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (18, 45) = 90
LCM of 18 and 45 Using Listing the Multiples
To calculate the LCM of 18 and 45 by listing out the common multiples, list the multiples as shown below
| Multiples of 18 | Multiples of 45 |
| 18 | 45 |
| 36 | 90 |
| 54 | 135 |
| 72 | 180 |
| 90 | 225 |
The smallest common multiple of 18 and 45 is 90.
Therefore LCM (18, 45) = 90
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LCM of 18 and 45 Solved Example
Question: The product of two numbers is 810. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 810
LCM × GCD = product of numbers
LCM = Product/GCD = 810/9
Therefore, the LCM is 90.
The probable combination for the given case is LCM(18, 45) = 90.
Frequently Asked Questions on LCM of 18 and 45
What is the LCM of 18 and 45?
List the methods used to find the LCM of 18 and 45.
What is the Relation Between GCF and LCM of 18, 45?
What is the Least Perfect Square Divisible by 18 and 45?
LCM of 18 and 45 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5] ⇒ Least perfect square divisible by each 18 and 45 = LCM(18, 45) × 2 × 5 = 900 [Square root of 900 = √900 = ±30] Therefore, 900 is the required number.
If the LCM of 45 and 18 is 90, Find its GCF.
Since the LCM of 45 and 18 = 90
⇒ 90 × GCF(45, 18) = 810
Therefore, the GCF (greatest common factor) = 810/90 = 9.
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