LCM of 25 and 45 is 225. LCM can be defined as the smallest positive number that is a multiple of two or more numbers. The full form of LCM is the least common multiple. Solving the problems with the help of the article Least Common Multiple (LCM) is the ultimate need for students who aspire to score excellent marks in exams. Students who want to learn the simple method of finding the least common multiple of given numbers using prime factorisation, division method and list of multiples can make use of this article prepared by experts in a simple language. In this article, let us grasp the method of determining the least common multiple of 25 and 45 in a precise manner.
What is LCM of 25 and 45?
The answer to this question is 225.
How to Find LCM of 25 and 45?
The LCM of 25 and 45 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25 and 45 Using Prime Factorisation Method
In the prime factorisation method, we can express the numbers as the product of prime numbers. Hence, the numbers 25 and 45 can be expressed as;
25 = 5 × 5
45 = 3 × 3 × 5
LCM (25, 45) = 3 × 3 × 5 × 5 = 225
LCM of 25 and 45 Using Division Method
In the division method, to calculate the LCM, we divide the numbers 25 and 45 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 45.
| 3 | 25 | 45 |
| 3 | 25 | 15 |
| 5 | 25 | 5 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (25, 45) = 3 × 3 × 5 × 5 = 225
LCM of 25 and 45 Using Listing the Multiples
Here, we list down the multiples of given numbers to find the lowest common multiple among them. Check the multiples of 25 and 45 from the table mentioned below.
| Multiples of 25 | Multiples of 45 |
| 25 | 45 |
| 50 | 90 |
| 75 | 135 |
| 100 | 180 |
| 125 | 225 |
| 150 | 270 |
| 175 | 315 |
| 200 | 360 |
| 225 | 405 |
| 250 | 450 |
LCM (25, 45) = 225
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 25 and 45?
Solution: 225 is the smallest number that is divisible by both 25 and 45.
Q. 2: The GCD and LCM of two numbers are 5 and 225. If one number is 25, what is the other number?
Solution: Let the other number be m.
We know that,
GCD × LCM = 25 × m
m = (GCD × LCM)/ 25
m = (5 × 225) / 25
m = 45
Hence, the other number is 45.
Frequently Asked Questions on LCM of 25 and 45
What is the LCM of 25 and 45?
Is the LCM of 25 and 45 the same as the HCF of 25 and 45?
125 is the LCM of 25 and 45. True or False.
What are the methods used to find the LCM of 25 and 45?
The methods used to find the LCM of 25 and 45 are
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 25 and 45 is 225?
GCF × LCM = 25 × 45
Given
LCM = 225
GCF × LCM = 25 × 45
GCF × 225 = 25 × 45
GCF = 5
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