LCM of 6 and 21 is 42. Least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. The article HCF and LCM explain the easiest method to find the HCF and LCM of given numbers. This article is the best reference guide for students who are looking for an inspiring learning experience. In this article, students can learn the simple format of representing the least common multiple of 6 and 21 with solved examples and FAQs.
What is LCM of 6 and 21?
The Least Common Multiple of 6 and 21 is 42.
How to Find LCM of 6 and 21?
We can obtain the LCM of 6 and 21 by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 6 and 21 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 6 and 21 can be denoted as;
6 = 2 × 3
21 = 3 × 7
LCM (6, 21) = 2 × 3 × 7 = 42
LCM of 6 and 21 Using Division Method
In the division method, we divide the numbers 6 and 21 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 6 and 21.
| 2 | 6 | 21 |
| 3 | 3 | 21 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (6, 21) = 2 × 3 × 7 = 42
LCM of 6 and 21 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. The below table represents the multiples of 6 and 21.
| Multiples of 6 | Multiples of 21 |
| 6 | 21 |
| 12 | 42 |
| 18 | 63 |
| 24 | 84 |
| 30 | 105 |
| 36 | 126 |
| 42 | 147 |
LCM (6, 21) = 42
Related Articles
- LCM calculator
- Prime Factorization and Division Method for LCM and HCF
- LCM Formula
- LCM with Examples
- Least Common Multiple (LCM)
- LCM of Two Numbers
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 6 and 21?
Solution: 42 is the smallest number that is divisible by both 6 and 21.
2. The GCD and LCM of the two numbers are 3 and 42. If one number is 21, calculate the other number.
Solution: Let the other number be p
We know that,
GCD × LCM = 21 × p
p = (GCD × LCM) / 21
p = (3 × 42) / 21
p = 6
Hence the other number is 6.
Frequently Asked Questions on LCM of 6 and 21
What is the LCM of 6 and 21?
What are the methods used to find the LCM of 6 and 21?
The following methods are used to find the LCM of 6 and 21:
Prime Factorisation
Division Method
Listing the Multiples
What is the LCM of 6 and 21 and the HCF of 6 and 21?
Find the GCF if the LCM of 6 and 21 is 42.
GCF × LCM = 6 × 21
Given
LCM = 42
GCF × 42 = 6 × 21
GCF = 3
Find the LCM of 6 and 21 using the prime factorisation method.
In this method, to find the LCM, we express the numbers as the product of prime factors
6 = 2 × 3
21 = 3 × 7
LCM (6, 21) = 2 × 3 × 7 = 42
Comments