LCM of 6 and 25 is 150. The least common multiple is defined as the smallest common multiple of two or more numbers. The simple method of determining the least common multiple of two numbers is explained in the article LCM of Two Numbers. This article is curated by experts with the intention to help students understand the concept of LCM in-depth. Let us learn how to find the least common multiple of 6 and 25 with solved examples and FAQs in a detailed manner.
What is LCM of 6 and 25?
The Least Common Multiple of 6 and 25 is 150.
How to Find LCM of 6 and 25?
We can find the LCM of 6 and 25 using the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 25 Using Prime Factorisation Method
By prime factorisation method, we can write 6 and 25 as the product of prime numbers, such that;
6 = 2 × 3
25 = 5 × 5
LCM (6, 25) = 2 × 3 × 5 × 5 = 150
LCM of 6 and 25 Using Division Method
Here, to calculate the LCM of 6 and 25, we divide the numbers 6 and 25 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 6 and 25.
| 2 | 6 | 25 |
| 3 | 3 | 25 |
| 5 | 1 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (6, 25) = 2 × 3 × 5 × 5 = 150
LCM of 6 and 25 Using Listing the Multiples
In the listing multiples method, we list out the multiples of 6 and 25 to determine the least common multiple of 6 and 25. The multiples of 6 and 25 are as follows:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ……….., 138, 144, 150, ……..
Multiples of 25: 25,50, 75, 100, 125, 150, …………
LCM (6, 25) = 150
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 6 and 25?
Solution: 150 is the smallest number that is divisible by both 6 and 25.
Q. 2: The GCD and LCM of the two numbers are 1 and 150 respectively. If one number is 6, calculate the other number.
Solution: Let the other number be z.
We know that,
GCD × LCM = 6 × z
z = (GCD × LCM) / 6
z = (1 × 150) / 6
z = 25
Hence the other number is 25.
Frequently Asked Questions on LCM of 6 and 25
What is the LCM of 6 and 25?
How do you find the LCM of 6 and 25 using prime factorisation?
6 = 2 × 3
25 = 5 × 5
LCM (6, 25) = 2 × 3 × 5 × 5 = 150
Hence the least common multiple of 6 and 25 using prime factorisation is 150
150 is the LCM of 6 and 25. True or False.
What are the methods to find the LCM of 6 and 25?
The methods used to find the LCM of 6 and 25 are as follows:
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 6 and 25 is 150?
Given LCM of 6 and 25 is 150
We know that
LCM × GCF = 6 × 25
150 × GCF = 6 × 25
GCF = 1
Hence the GCF is 1
Comments