LCM of 25 and 40 is 200. In Maths, the LCM is used to add or subtract any two fractions when the denominators of the fractions are different. Learning the LCM concept thoroughly helps students to simplify the problems with ease. Students can make use of Least Common Multiple (LCM) article as the reference guide to grasp the in-depth knowledge relying on LCM accurately. Let us find the least common multiple of 25 and 40 using prime factorisation, division method and listing multiples in a detailed manner in this article.
What is LCM of 25 and 40?
The answer to this question is 200.
How to Find LCM of 25 and 40?
The LCM of 25 and 40 can be determined by the following methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 25 and 40 Using Prime Factorisation Method
By prime factorisation method, we can write 25 and 40 as the product of prime numbers, such that;
25 = 5 × 5
40 = 2 × 2 × 2 × 5
LCM (25, 40) = 2 × 2 × 2 × 5 × 5 = 200
LCM of 25 and 40 Using Division Method
In this method, to find the LCM, we divide the numbers 25 and 40 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 25 and 40.
| 2 | 25 | 40 |
| 2 | 25 | 20 |
| 2 | 25 | 10 |
| 5 | 25 | 5 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (25, 40) = 2 × 2 × 2 × 5 × 5 = 200
LCM of 25 and 40 Using Listing the Multiples
To determine the least common multiple of 25 and 40 using listing multiples, we list out the multiples of 25 and 40. The below table shows the multiples of 25 and 40.
| Multiples of 25 | Multiples of 40 |
| 25 | 40 |
| 50 | 80 |
| 75 | 120 |
| 100 | 160 |
| 125 | 200 |
| 150 | 240 |
| 175 | 280 |
| 200 | 320 |
| 225 | 360 |
LCM (25, 40) = 200
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 40?
Solution: 200 is the smallest number that is divisible by both 25 and 40.
Q. 2: What is the GCF of 25 and 40?
Solution: The GCF of 25 and 40 is 5.
Frequently Asked Questions on LCM of 25 and 40
What is the LCM of 25 and 40?
Is the LCM of 25 and 40 the same as the HCF of 25 and 40?
How do you find the LCM of 25 and 40 by prime factorisation?
25 = 5 × 5
40 = 2 × 2 × 2 × 5
LCM (25, 40) = 2 × 2 × 2 × 5 × 5 = 200
Therefore the least common multiple of 25 and 40 by prime factorisation is 200.
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