LCM of 25 and 75 is 75. The number evenly divisible by 25 and 75 provides the LCM value. Least common multiples of 25 and 75 are determined using the common multiples. (25, 50, 75, 100, 125, 150, 175, ….) and (75, 150, 225, 300,….) are the multiples of 25 and 75. The LCM of two numbers using the prime factorization, division and by listing the multiples are explained in a stepwise format for a better conceptual knowledge among the students.
Also read: Least common multiple
What is LCM of 25 and 75?
The answer to this question is 75. The LCM of 25 and 75 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 25 and 75, is the smallest positive integer 75 which is divisible by both 25 and 75 with no remainder.
How to Find LCM of 25 and 75?
LCM of 25 and 75 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25 and 75 Using Prime Factorisation Method
The prime factorisation of 25 and 75, respectively, is given by:
25 = 5 x 5 = 5²
75 = 3 x 5 x 5 = 3¹ x 5²
LCM (25, 75) = 75
LCM of 25 and 75 Using Division Method
We’ll divide the numbers (25, 75) by their prime factors to get the LCM of 25 and 75 using the division method (preferably common). The LCM of 25 and 75 is calculated by multiplying these divisors.
|
3 |
25 |
75 |
|
5 |
25 |
25 |
|
5 |
5 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (25, 75) = 75
LCM of 25 and 75 Using Listing the Multiples
To calculate the LCM of 25 and 75 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 25 |
Multiples of 75 |
|
25 |
75 |
|
50 |
150 |
|
75 |
225 |
|
100 |
300 |
LCM (25, 75) = 75
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 25 and 75 Solved Examples
Question: What is the smallest number which is exactly divisible by 25 and 75?
Solution:
We know that
The smallest number which is exactly divisible by 25 and 75 is the LCM.
Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, ….
Multiples of 75 = 75, 150, 225, 300,….
Hence, the LCM of 25 and 75 is 75.
Frequently Asked Questions on LCM of 25 and 75
What is the LCM of 25 and 75 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
25 = 5 x 5 = 5²
75 = 3 x 5 x 5 = 3¹ x 5²
LCM of 25 and 75 is the product of prime factors raised to the highest exponent among the numbers 25 and 75
LCM of 25 and 75 = 75
If the LCM of 25 and 75 is 75, find the GCF.
LCM x GCF = 25 x 75
Given
LCM of 25 and 75 = 75
75 x GCF = 1875
GCF = 1875/75 = 25
Show the relation between GCF and LCM of 25 and 75.
The relation between GCF and LCM of 25 and 75 is
LCM x GCF = 25 x 75
LCM x GCF = 1875
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