LCM of 18 and 30 is 90. Students can learn how to get the least common multiple of 18 and 30 from the common multiples. (18, 36, 54, 72, ….) and (30, 60, 90, 120,….) are the multiples of 18 and 30. The methods used to find the LCM of two numbers are prime factorisation, division and by listing the multiples. The step-wise explanation is provided here for the students’ reference.
Also read: Least common multiple
What is LCM of 18 and 30?
The answer to this question is 90. The LCM of 18 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 30, is the smallest positive integer 90 which is divisible by both 18 and 30 with no remainder.
How to Find LCM of 18 and 30?
LCM of 18 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 30 Using Prime Factorisation Method
The prime factorisation of 18 and 30, respectively, is given by:
18 = 2 x 3 x 3 = 2¹ x 3²
30 = 2 x 3 x 5 = 2¹ x 3¹ x 5¹
LCM (18, 30) = 90
LCM of 18 and 30 Using Division Method
We’ll divide the numbers (18, 30) by their prime factors to get the LCM of 18 and 30 using the division method (preferably common). The LCM of 18 and 30 is calculated by multiplying these divisors.
| 2 | 18 | 30 |
| 3 | 9 | 15 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (18, 30) = 90
LCM of 18 and 30 Using Listing the Multiples
To calculate the LCM of 18 and 30 by listing out the common multiples, list the multiples as shown below
| Multiples of 18 | Multiples of 30 |
| 18 | 30 |
| 36 | 60 |
| 54 | 90 |
| 72 | 120 |
| 90 | 150 |
| 108 | 180 |
The smallest common multiple of 18 and 30 is 90.
Therefore LCM (18, 30) = 90
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Video Lesson on Applications of LCM
LCM of 18 and 30 Solved Example
Question: Determine the LCM if the product of two numbers is 540 and the GCD is 6.
Solution:
It is given that,
Product of two numbers = 540
GCD = 6
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 540/6
LCM = 90
Hence, the LCM is 90.
Frequently Asked Questions on LCM of 18 and 30
How to find the LCM of 18 and 30?
Write the methods to get the LCM of 18 and 30.
If the LCM of 18 and 30 is 90, what is the GCF?
LCM x GCF = 18 x 30
Given
LCM of 18 and 30 = 90
90 x GCF = 540
GCF = 540/90 = 6
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