LCM of 3 and 7 is 21. The technique to find the smallest common multiple between any two or more numbers is known as Least Common Multiple. To obtain in-depth knowledge based on LCM of two numbers, students can refer to LCM of Two Numbers as it is the best study guide as per the expert teachers. Learn how to find the least common multiple of 3 and 7 in a detailed manner along with examples and FAQs in this article.
What is LCM of 3 and 7?
The answer to this question is 21.
How to Find LCM of 3 and 7?
LCM of 3 and 7 can be determined by using the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 7 Using Prime Factorisation Method
We can find the LCM of 3 and 7 using prime factorisation by multiplying prime factors raised to their respective highest power.
3 = 3
7 = 7
LCM (3, 7) = 21
LCM of 3 and 7 Using Division Method
Here, we divide the numbers 3 and 7 by their prime factors to calculate their LCM. The product of these divisors gives the least common multiple of 3 and 7.
|
3 |
3 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (3, 7) = 3 × 7 = 21
LCM of 3 and 7 Using Listing the Multiples
In this method, we list the multiples of 3 and 7 to determine their least common multiple. The following table shows the multiples of 3 and 7.
|
Multiples of 3 |
Multiples of 7 |
|
3 |
7 |
|
6 |
14 |
|
9 |
21 |
|
12 |
28 |
|
15 |
35 |
|
18 |
42 |
|
21 |
49 |
LCM (3, 7) = 21
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Calculate the LCM if the product of two numbers is 21 and their GCD is 1.
Solution: Given
GCD = 1
Product of numbers = 21
LCM × GCD = Product of numbers
LCM = Product of numbers/GCD
LCM = 21/1
LCM = 21
Therefore the LCM is 21.
Q. 2: Find the LCM of 3 and 7 using the listing multiples.
Solution: First list out the multiples of 3 and 7
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, …..
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63,…..
Here the LCM is 21
Thus the LCM of 3 and 7 is 21.
Frequently Asked Questions on LCM of 3 and 7
What is the LCM of 3 and 7?
List out the methods used to find the LCM of 3 and 7.
The methods used to find the LCM of 3 and 7 are as follows:
Prime Factorization Method
Listing the Multiples
Division Method
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