LCM of 8 and 25 is 200. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 8 and 25, the LCM of 8 and 25 is the smallest value. (8, 16, 24, 32, 40, 48, 56, etc.) and (25, 50, 75, 100, etc.) are the first few multiples of 8 and 25 respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 8 and 25?
The answer to this question is 200. The LCM of 8 and 25 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8 and 25, is the smallest positive integer 200 which is divisible by both 8 and 25 with no remainder.
How to Find LCM of 8 and 25?
LCM of 8 and 25 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 25 Using Prime Factorisation Method
The prime factorisation of 8 and 25, respectively, is given by:
8 = (2 × 2 × 2) = 23 and
25 = (5 × 5) = 52
LCM (24, 36) = 72
LCM of 8 and 25 Using Division Method
We’ll divide the numbers (8, 25) by their prime factors to get the LCM of 8 and 25 using the division method (preferably common). The LCM of 8 and 25 is calculated by multiplying these divisors.
| 2 | 8 | 25 |
| 2 | 4 | 25 |
| 2 | 2 | 25 |
| 5 | 1 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (8, 25) = 200
LCM of 8 and 25 Using Listing the Multiples
To calculate the LCM of 8 and 25 by listing out the common multiples, list the multiples as shown below
| Multiples of 8 | Multiples of 25 |
| 8 | 25 |
| 16 | 50 |
| 24 | 75 |
| 32 | 100 |
| 40 | 125 |
| 48 | 150 |
| ……. | 175 |
| 200 | 200 |
The smallest common multiple of 8 and 25 is 200.
Therefore LCM (8, 25) = 200
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LCM of 8 and 25 Solved Example
Question: The GCD and LCM of two numbers are 1 and 200 respectively. If one number is 25, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 25 × b
⇒ b = (GCD × LCM)/25
⇒ b = (1 × 200)/25
⇒ b = 8
Frequently Asked Questions on LCM of 8 and 25
What is the LCM of 8 and 25?
List the methods used to find the LCM of 8 and 25.
If the LCM of 25 and 8 is 200, Find its GCF.
Since the LCM of 25 and 8 = 200
⇒ 200 × GCF(25, 8) = 200
Therefore, the GCF (greatest common factor) = 200/200 = 1.
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