LCM of 25 and 100 is 100. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. The article HCF and LCM is designed by experts to improve students’ logical approach and rational thinking abilities. This article, in simple language, is the best study material for effective learning of the concept. Learn how to verify the least common multiple of 25 and 100 with the help of solved examples and FAQs.
What is LCM of 25 and 100?
The Least Common Multiple of 25 and 100 is 100.
How to Find LCM of 25 and 100?
The LCM of 25 and 100 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 25 and 100 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 25 and 100 can be represented as;
25 = 5 × 5
100 = 2 × 2 × 5 × 5
LCM (25, 100) = 2 × 2 × 5 × 5 = 100
LCM of 25 and 100 Using Division Method
In the division method, we divide the numbers 25 and 100 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 25 and 100.
| 2 | 25 | 100 |
| 2 | 25 | 50 |
| 5 | 25 | 25 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (25, 100) = 2 × 2 × 5 × 5 = 100
LCM of 25 and 100 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. The below table represents the multiples of 25 and 100.
| Multiples of 25 | Multiples of 100 |
| 25 | 100 |
| 50 | 200 |
| 75 | 300 |
| 100 | 400 |
| 125 | 500 |
LCM (25, 100) = 100
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 25 and 100?
Solution: 100 is the smallest number that is divisible by both 25 and 100.
2. What is the LCM if the product of two numbers is 2500 and their GCD is 25?
Solution: Given
GCD = 25
Product of numbers = 2500
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 2500/25
LCM = 100
Hence the LCM is 100.
Frequently Asked Questions on LCM of 25 and 100
What is the LCM of 25 and 100?
What are the methods used to find the LCM of 25 and 100?
The following methods are used to find the LCM of 25 and 100:
Prime Factorisation
Division Method
Listing the Multiples
120 is the LCM of 25 and 100. True or False.
Calculate the GCF if the LCM of 25 and 100 is 100.
GCF × LCM = 25 × 100
Given
LCM = 100
GCF × 100 = 25 × 100
GCF = 25
How to find the LCM of 25 and 100 using the prime factorisation method?
In this method, we express the numbers as the product of prime factors
25 = 5 × 5
100 = 2 × 2 × 5 × 5
LCM (25, 100) = 2 × 2 × 5 × 5 = 100
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