LCM of 8 and 18 is 72. In Mathematics, the LCM of two numbers is the value that is evenly divisible by the two given numbers. Least common multiple of 8 and 18 is the smallest number we obtain from the common multiples. (8, 16, 24, 32, 40, ….) and (18, 36, 54, 72, 90,….) are the multiples of 8 and 18. We can get the LCM easily using various methods like prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 8 and 18?
The answer to this question is 72. The LCM of 8 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 18, is the smallest positive integer 72 which is divisible by both 8 and 18 with no remainder.
How to Find LCM of 8 and 18?
LCM of 8 and 18 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 18 Using Prime Factorisation Method
The prime factorisation of 8 and 18, respectively, is given by:
8 = 2 x 2 x 2 = 2³
18 = 2 x 3 x 3 = 2¹ x 3²
LCM (8, 18) = 72
LCM of 8 and 18 Using Division Method
We’ll divide the numbers (8, 18) by their prime factors to get the LCM of 8 and 18 using the division method (preferably common). The LCM of 8 and 18 is calculated by multiplying these divisors.
2 | 8 | 18 |
2 | 4 | 9 |
2 | 2 | 9 |
3 | 1 | 9 |
3 | 1 | 3 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (8, 18) = 72
LCM of 8 and 18 Using Listing the Multiples
To calculate the LCM of 8 and 18 by listing out the common multiples, list the multiples as shown below
Multiples of 8 | Multiples of 18 |
8 | 18 |
16 | 36 |
24 | 54 |
32 | 72 |
40 | 90 |
48 | 108 |
56 | 126 |
64 | 144 |
72 | 162 |
80 | 180 |
The smallest common multiple of 8 and 18 is 72.
Therefore LCM (8, 18) = 72
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Video Lesson on Applications of LCM
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LCM of 8 and 18 Solved Example
Question: What is the LCM if the product of two numbers is 144 and the GCD is 2?
Solution:
It is given that
Product of two numbers = 144
GCD = 2
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 144/2
LCM = 72
Hence, the LCM is 72.
Frequently Asked Questions on LCM of 8 and 18
What is the LCM of 8 and 18?
Mention the methods used to determine the LCM of 8 and 18.
Calculate the GCF if the LCM of 8 and 18 is 72.
LCM x GCF = 8 x 18
Given
LCM of 8 and 18 = 72
72 x GCF = 144
GCF = 144/72 = 2
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