LCM of 21 and 25 is 525. LCM depicts the least common factor or multiple of any two or more given numbers. Students can learn the LCM concept thoroughly by using the article LCM with Examples crafted by experts in an understandable language. This article explains the LCM concept in a comprehensive manner with suitable examples for effective learning. Students can access this article in both offline and online modes whenever required. Let us learn the simple format of determining the least common multiple of 21 and 25 in this article.
What is LCM of 21 and 25?
The Least Common Multiple of 21 and 25 is 525.
How to Find LCM of 21 and 25?
LCM of 21 and 25 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 21 and 25 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 21 and 25 are expressed as;
21 = 3 × 7
25 = 5 × 5
LCM (21, 25) = 3 × 5 × 5 × 7 = 525
LCM of 21 and 25 Using Division Method
In the division method, to find the least common multiple of 21 and 25, we divide the numbers 21 and 25 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 21 and 25.
| 3 | 21 | 25 |
| 5 | 7 | 25 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (21, 25) = 3 × 5 × 5 × 7 = 525
LCM of 21 and 25 Using Listing the Multiples
In this method, we list down the multiples of given numbers to calculate the lowest common multiple among them. The multiples of 21 and 25 are given below:
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, ………, 483, 504, 525,……….
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, ………, 475, 500, 525,……….
LCM (21, 25) = 525
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 21 and 25?
Solution: 525 is the smallest number that is divisible by both 21 and 25.
2. The GCD and LCD of the two numbers are 1 and 525. If one number is 21, what is the other number?
Solution: Let the other number be k
GCD × LCM = 21 × k
k = (GCD × LCM) / 21
k = (1 × 525) / 21
k = 25
Hence, the other number is 25.
Frequently Asked Questions on LCM of 21 and 25
What is the LCM of 21 and 25?
Is the LCM of 21 and 25 the same as the HCF of 21 and 25?
425 is the LCM of 21 and 25. True or False.
What are the methods used to find the LCM of 21 and 25?
The methods used to find the LCM of 21 and 25 are
Prime Factorisation
Division Method
Listing the Multiples
Calculate the GCF if the LCM of 21 and 25 is 525.
GCF × LCM = 21 × 25
Given
LCM = 525
GCF × 525 = 21 × 25
GCF = 1
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