LCM of 18 and 40 is 360. Learn how the LCM of 18 and 40 can be found by referring to this article. The least common multiple of 18 and 40 is the smallest number which is evenly divisible by the given two numbers. The multiples of 18 are (18, 36, 54, 72, 90, 108, 126, ….) and the multiples of 40 are (40, 80, 120, 160, 200, ….) respectively. Division, Prime factorisation and listing of the multiples are the methods we can use to get the LCM.
Also read: Least common multiple
What is LCM of 18 and 40?
The answer to this question is 360. The LCM of 18 and 40 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 40, is the smallest positive integer 360 which is divisible by both 18 and 40 with no remainder.
How to Find LCM of 18 and 40?
LCM of 18 and 40 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 40 Using Prime Factorisation Method
The prime factorisation of 18 and 40, respectively, is given by:
18 = 2 x 3 x 3 = 2¹ x 3²
40 = 2 x 2 x 2 x 5 = 2³ x 5¹
LCM (18, 40) = 360
LCM of 18 and 40 Using Division Method
We’ll divide the numbers (18, 40) by their prime factors to get the LCM of 18 and 40 using the division method (preferably common). The LCM of 18 and 40 is calculated by multiplying these divisors.
|
2 |
18 |
40 |
|
2 |
9 |
20 |
|
2 |
9 |
10 |
|
3 |
9 |
5 |
|
3 |
3 |
5 |
|
5 |
1 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (18, 40) = 360
LCM of 18 and 40 Using Listing the Multiples
To calculate the LCM of 18 and 40 by listing out the common multiples, list the multiples as shown below
Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, . . . ., 306, 324, 342, 360, . . . .
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 240, 280, 320, 360, . . . .
LCM (18, 40) = 360
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LCM of 18 and 40 Solved Examples
Question: If the product of two numbers is 720, calculate the LCM if the GCD is 2.
Solution:
It is given that,
GCD = 2
Product of two numbers = 720
We know that;
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 720/2
LCM = 360
Hence, the LCM is 360.
Frequently Asked Questions on LCM of 18 and 40
What is the LCM of 18 and 40?
If the LCM of 18 and 40 is 360, determine the GCF.
LCM x GCF = 18 x 40
Given
LCM of 18 and 40 is 360
360 x GCF = 720
GCF = 720/360 = 2
What are the methods used to find the LCM of 18 and 40?
The methods used to find the LCM of 18 and 40 are:
Division method
Prime Factorisation
Listing the multiples
The LCM and GCD of two numbers are 360 and 2. If one number is 18, determine the other.
Consider x as the other number.
GCD x LCM = 18 x x
x = (GCD x LCM)/ 18
x = (2 x 360)/18
x = 40
Hence, the other number is 40.
What is the relation between LCM and GCF of 18 and 40?
The relation between LCM and GCF of 18 and 40 is
LCM x GCF = 18 x 40
LCM x GCF = 720
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