LCM of 18 and 25 is 450. The number which equally divides 18 and 25 gives the LCM. The common multiples of 18 and 25 will help to get the least common multiple of 18 and 25. The multiples of 18 are (18, 36, 54, 72, 90, ….) and the multiples of 25 are (25, 50, 75, 100, 125, 150, …..) respectively. For a good knowledge of the LCM concept and methods such as prime factorisation method, division method and listing of the multiples, this article is very crucial.
Also read: Least common multiple
What is LCM of 18 and 25?
The answer to this question is 450. The LCM of 18 and 25 using various methods are shown in this article for your reference. The LCM of two non-zero integers, 18 and 25, is the smallest positive integer 450 which is divisible by both 18 and 25 with no remainder.
How to Find LCM of 18 and 25?
LCM of 18 and 25 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 25 Using Prime Factorisation Method
The prime factorisation of 18 and 25, respectively, is given by:
18 = 2 x 3 x 3 = 2¹ x 3²
25 = 5 x 5 = 5²
LCM (18, 25) = 450
LCM of 18 and 25 Using Division Method
We’ll divide the numbers (18, 25) by their prime factors to get the LCM of 18 and 25 using the division method (preferably common). The LCM of 18 and 25 is calculated by multiplying these divisors.
|
2 |
18 |
25 |
|
3 |
9 |
25 |
|
3 |
3 |
25 |
|
5 |
1 |
25 |
|
5 |
1 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (18, 25) = 450
LCM of 18 and 25 Using Listing the Multiples
To calculate the LCM of 18 and 25 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, . . . ., 414, 432, 450, . . . .
Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 400, 425, 450, . . . .
LCM (18, 25) = 450
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Video Lesson on Applications of LCM
LCM of 18 and 25 Solved Examples
Question: If the product of two numbers is 450 and the GCD is 1, find the LCM.
Solution:
Given
Product of two numbers = 450
GCD = 1
LCM x GCF = Product
LCM = Product/GCD
LCM = 450/1
LCM = 450
Hence, the LCM is 450.
Frequently Asked Questions on LCM of 18 and 25
Find the GCF if the LCM of 18 and 25 is 450.
We know that
LCM x GCF = 18 x 25
As LCM (18, 25) is 450
450 x GCF = 450
GCF = 450/450 = 1
Determine the LCM of 18 and 25.
Show the relation between GCF and LCM of 18 and 25.
The relation between GCF and LCM of 18 and 25 is:
LCM x GCF = 18 x 25
LCM x GCF = 450
The LCM and GCD of two numbers are 450 and 1. If 25 is one number, find the other.
Consider the other number as y
GCD x LCM = 25 x y
y = (GCD x LCM)/25
y = (1 x 450)/25
y = 18
Hence, the other number is 18.
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