LCM of 3 and 21 is 21. LCM is the method to find the smallest possible multiple of two or more numbers. The good hold on the LCM concept is important so that students solve tricky problems with ease. Experts curated the article LCM of Two Numbers to improve conceptual knowledge among students. Let us learn in detail how to calculate the least common multiple of 3 and 21 using prime factorisation, division method and a list of multiples in a detailed manner.
What is LCM of 3 and 21?
The Least Common Multiple of 3 and 21 is 21.
How to Find LCM of 3 and 21?
LCM of 3 and 21 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 3 and 21 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 3 and 21 can be expressed as;
3 = 3
21 = 3 × 7
LCM (3, 21) = 3 × 7 = 21
LCM of 3 and 21 Using Division Method
In the division method, to calculate the least common multiple of 3 and 21, we divide the numbers 3 and 21 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 3 and 21.
| 3 | 3 | 21 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (3, 21) = 3 × 7 = 21
LCM of 3 and 21 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. Check the multiples of 3 and 21 from the table mentioned below.
| Multiples of 3 | Multiples of 21 |
| 3 | 21 |
| 6 | 42 |
| 9 | 63 |
| 12 | 84 |
| 15 | 105 |
| 18 | 126 |
| 21 | 147 |
| 24 | 168 |
LCM (3, 21) = 21
Related Articles
- Least Common Multiple (LCM)
- HCF and LCM
- Prime Factorization and Division Method for LCM and HCF
- LCM Calculator
- LCM with Examples
- LCM Formula
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 3 and 21?
Solution: 21 is the smallest number that is divisible by both 3 and 21.
2. The product of the two numbers is 63. Find the LCM if their GCD is 3.
Solution: Given
GCD = 3
Product of numbers = 63
We know that
GCF × LCM = Product of numbers
LCM = Product of numbers / GCF
LCM = 63 / 3
LCM = 21
Hence the LCM is 21.
Frequently Asked Questions on LCM of 3 and 21
What is the LCM of 3 and 21?
Mention the LCM of 3 and 21 and the HCF of 3 and 21.
Name the methods used to find the LCM of 3 and 21.
The methods used to find the LCM of 3 and 21 are as follows:
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 3 and 21 using prime factorisation.
In this method, we write the numbers as the product of prime factors to find the LCM
3 = 3
21 = 3 × 7
LCM (3, 21) = 3 × 7 = 21
What is the GCF if the LCM of 3 and 21 is 21?
GCF × LCM = 3 × 21
Given
LCM = 21
GCF × 21 = 3 × 21
GCF = 3
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