LCM of 9 and 18 is 18. The common multiple which is divisible evenly by the given numbers is the LCM. The least common multiple of 9 and 18 can be found from the smallest common multiples. (9, 18, 27, 36, 45, ….) are the multiples of 9 and (18, 36, 54, 72, 90, ….) are the multiples of 18 respectively. Division, prime factorisation and listing the multiples are the methods used to find the LCM.
Also read: Least common multiple
What is LCM of 9 and 18?
The answer to this question is 18. The LCM of 9 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 18, is the smallest positive integer 18 which is divisible by both 9 and 18 with no remainder.
How to Find LCM of 9 and 18?
LCM of 9 and 18 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 18 Using Prime Factorisation Method
The prime factorisation of 9 and 18, respectively, is given by:
9 = 3 x 3 = 3²
18 = 2 x 3 x 3 = 2¹ x 3²
LCM (9, 18) = 18
LCM of 9 and 18 Using Division Method
We’ll divide the numbers (9, 18) by their prime factors to get the LCM of 9 and 18 using the division method (preferably common). The LCM of 9 and 18 is calculated by multiplying these divisors.
2 | 9 | 18 |
3 | 9 | 9 |
3 | 3 | 3 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 18) = 18
LCM of 9 and 18 Using Listing the Multiples
To calculate the LCM of 9 and 18 by listing out the common multiples, list the multiples as shown below
Multiples of 9 | Multiples of 18 |
9 | 18 |
18 | 36 |
27 | 54 |
36 | 72 |
45 | 90 |
54 | – |
LCM (9, 18) = 18
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Video Lesson on Applications of LCM
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LCM of 9 and 18 Solved Example
Question: The product of two numbers is 162. If the GCD is 9, find the LCM.
Solution:
Given
GCF = 9
Product of two numbers = 162
We know that;
LCM x GCD = product of two numbers
LCM x 9 = 162
LCM = 162/9 = 18
Therefore, the LCM is 18.
Frequently Asked Questions on LCM of 9 and 18
What is the LCM of 9 and 18?
Find the GCF if the LCM of 9 and 18 is 18.
LCM x GCF = 9 x 18
Given
LCM of 9 and 18 is 18
18 x GCF = 162
GCF = 162/18 = 9
What are the methods used to find the LCM of 9 and 18?
The methods used to find the LCM of 9 and 18 are
Listing the multiples
Prime Factorisation
Division method
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