LCM of 10 and 25 is 50. The least common multiple is the smallest common multiple of two or more numbers. LCM of Two Numbers article is designed by experts with the aim to provide a strong base of fundamental topics which are essential for the exam. This article also helps students to obtain problem-solving and time management skills, which are very important to secure more marks in exams. In this article, we will discuss how to find the least common multiple of 10 and 25 in a precise manner.
What is LCM of 10 and 25?
The Least Common Multiple of 10 and 25 is 50.
How to Find LCM of 10 and 25?
The LCM of 10 and 25 can be determined by the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 25 Using Prime Factorisation Method
In the prime factorisation method, we can obtain the LCM of 10 and 25 by multiplying prime factors raised to their respective highest power.
10 = 2 × 5
25 = 5 × 5
LCM (10, 25) = 2 × 5 × 5 = 50
LCM of 10 and 25 Using Division Method
We divide the numbers 10 and 25 by their prime factors until we get the result as one in the complete row to calculate the LCM of 10 and 25 by the division method. The product of these divisors represents the LCM of 10 and 25. This can be done as below.
| 2 | 10 | 25 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 25) = 2 × 5 × 5 = 50
LCM of 10 and 25 Using Listing the Multiples
To find the least common multiple of 10 and 25 using listing multiples, we list out the multiples of 10 and 25. The following table shows the multiples of 10 and 25.
| Multiples of 10 | Multiples of 25 |
| 10 | 25 |
| 20 | 50 |
| 30 | 75 |
| 40 | 100 |
| 50 | 125 |
| 60 | 150 |
LCM (10, 25) = 50
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 10 and 25?
Solution: 50 is the smallest number that is divisible by both 10 and 25.
Q. 2: The GCD and LCM of the two numbers are 5 and 50 respectively. If one number is 10, calculate the other number.
Solution: Let us consider the other number as p
We know that,
GCD × LCM = 10 × p
p = (GCD × LCM) / 10
p = (5 × 50) / 10
p = 25
Hence the other number is 25.
Frequently Asked Questions on LCM of 10 and 25
What is the LCM of 10 and 25?
List out the methods used to find the LCM of 10 and 25.
The methods used to find the LCM of 10 and 25 are
Prime Factorisation
Division Method
Listing the Multiples
Is the LCM of 10 and 25 the same as the HCF of 10 and 25?
What is the GCF if the LCM of 10 and 25 is 50?
Given
LCM of 10 and 25 is 50
We know that
LCM × GCF = 10 × 25
50 × GCF = 250
GCF = 250 / 50
GCF = 5
How do you find the LCM of 10 and 25 using the prime factorisation method?
In this method, we find the prime factors of given numbers to determine the LCM.
10 = 2 × 5
25 = 5 × 5
LCM (10, 25) = 2 × 5 × 5 = 50
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