LCM of 12 and 25 is 300. LCM depicts the least common factor or multiple of any two or more given numbers. Experts formulated the article LCM with Examples in a precise manner to help students with the best material for effective learning of the concept. This article provides more clarity on the LCM concept with suitable examples. Let us learn how to calculate the least common multiple of 12 and 25 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 12 and 25?
The Least Common Multiple of 12 and 25 is 300.
How to Find LCM of 12 and 25?
The LCM of 12 and 25 can be obtained by using the methods given below:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 12 and 25 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 12 and 25 are expressed as;
12 = 2 × 2 × 3
25 = 5 × 5
LCM (12, 25) = 2 × 2 × 3 × 5 × 5 = 300
LCM of 12 and 25 Using Division Method
In the division method, to calculate the least common multiple of 12 and 25, we divide the numbers 12 and 25 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 12 and 25.
| 2 | 12 | 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 (12, 25) = 2 × 2 × 3 × 5 × 5 = 300
LCM of 12 and 25 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. Let us glance at the multiples of 12 and 25 given below.
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ……….
Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, …….
LCM (12, 25) = 300
Related Articles
Prime Factorisation 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 12 and 25?
Solution: 300 is the smallest number that is divisible by both 12 and 25.
2. The GCD and LCM of two numbers are 1 and 300. If one number is 25, what is the other number?
Solution: Let the other number be k
We know that,
GCD × LCM = 25 × k
k = (GCD × LCM) / 25
k = (1 × 300) / 25
k = 12
Hence the other number is 12.
Frequently Asked Questions on LCM of 12 and 25
What is the LCM of 12 and 25?
Is the LCM of 12 and 25 the same as the HCF of 12 and 25?
Is 500 the LCM of 12 and 25?
Name the methods used to find the LCM of 12 and 25.
The methods used to find the LCM of 12 and 25 are
Prime Factorisation
Division Method
Listing the Multiples
Calculate the GCF if the LCM of 12 and 25 is 300.
GCF × LCM = 12 × 25
Given
LCM = 300
GCF × 300 = 12 × 25
GCF = 1
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