LCM of 25 and 60 is 300. In Maths, the LCM of two numbers is the value we get when it is divisible evenly by the given numbers. Least common multiple of 25 and 60 is the smallest number we get from the common multiples. (25, 50, 75, 100, 125, ….) and (60, 120, 180, 240, 300, 360,….) are the multiples of 25 and 60. The LCM value can be found effortlessly using different methods like prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 25 and 60?
The answer to this question is 300. The LCM of 25 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 25 and 60, is the smallest positive integer 300 which is divisible by both 25 and 60 with no remainder.
How to Find LCM of 25 and 60?
LCM of 25 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25 and 60 Using Prime Factorisation Method
The prime factorisation of 25 and 60, respectively, is given by:
25 = 5 x 5 = 5²
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
LCM (25, 60) = 300
LCM of 25 and 60 Using Division Method
We’ll divide the numbers (25, 60) by their prime factors to get the LCM of 25 and 60 using the division method (preferably common). The LCM of 25 and 60 is calculated by multiplying these divisors.
|
2 |
25 |
60 |
|
2 |
25 |
30 |
|
3 |
25 |
15 |
|
5 |
25 |
5 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (25, 60) = 300
LCM of 25 and 60 Using Listing the Multiples
To calculate the LCM of 25 and 60 by listing out the common multiples, list the multiples as shown below
Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, ……
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, …….
The smallest common multiple of 25 and 60 is 300.
Therefore LCM (25, 60) = 300
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Video Lesson on Applications of LCM
LCM of 25 and 60 Solved Examples
Question: Calculate the LCM if the product of two numbers is 1500 and the GCD is 5.
Solution:
It is given that
Product of two numbers = 1500
GCD = 5
We know that
LCM x GCD = Product of two numbers
LCM = Product/GCD
LCM = 1500/5
LCM = 300
Hence, the LCM is 300.
Frequently Asked Questions on LCM of 25 and 60
What is the LCM of 25 and 60?
What are the methods used to find the LCM of 25 and 60?
Find the GCF if the LCM of 25 and 60 is 300.
LCM x GCF = 25 x 60
Given
LCM of 25 and 60 = 300
300 x GCF = 1500
GCF = 1500/300 = 5
The LCM and GCD of two numbers are 300 and 5. Find the other number if one number is 25.
Consider m as the other number
GCD x LCM = 25 x m
m = (GCD x LCM)/ 25
m = (5 x 300)/ 25
m = 60
Show the relation between GCF and LCM of 25 and 60.
The relation between GCF and LCM of 25 and 60 is
GCF x LCM = 25 x 60
GCF x LCM = 1500
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