LCM of 3 and 13 is 39. LCM is the smallest number that is a common multiple of a given set of numbers. HCF and LCM article provides an in-depth explanation of how to verify the LCM and HCF of given numbers using the prime factorisation and division method. Students who intend to gain proficiency in solving problems relying on LCM and HCF are recommended to follow this article on a daily basis. Let us have a look at how to find the least common multiple of 3 and 13 with the help of solved examples and FAQs in this article.
What is LCM of 3 and 13?
The Least Common Multiple of 3 and 13 is 39.
How to Find LCM of 3 and 13?
We can find the LCM of 3 and 13 by using the methods given below:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 3 and 13 Using Prime Factorisation Method
In the prime factorisation method, we can find the least common multiple of 3 and 13 by multiplying prime factors as shown below:
3 = 3
13 = 13
LCM (3, 13) = 3 × 13 = 39
LCM of 3 and 13 Using Division Method
In the division method, to calculate the least common multiple of 3 and 13, we divide the numbers 3 and 13 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 3 and 13.
| 3 | 3 | 13 |
| 13 | 1 | 13 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (3, 13) = 3 × 13 = 39
LCM of 3 and 13 Using Listing the Multiples
In this method, we list down the multiples of given numbers to calculate the lowest common multiple among them. Check the multiples of 3 and 13 from the table mentioned below.
| Multiples of 3 | Multiples of 13 |
| 3 | 13 |
| 6 | 26 |
| 9 | 39 |
| 12 | 52 |
| 15 | 65 |
| 18 | 78 |
| 21 | 91 |
| 24 | 104 |
| 27 | 117 |
| 30 | 130 |
| 33 | 143 |
| 36 | 156 |
| 39 | 169 |
LCM (3, 13) = 39
Related Articles
- Lowest Common Multiple (LCM)
- Prime Factorisation and Division Method for LCM and HCF
- LCM of Two Numbers
- LCM calculator
- LCM Formula
- LCM with Examples
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 3 and 13?
Solution: 39 is the smallest number that is divisible by both 3 and 13.
2. The GCD and LCM of the two numbers are 1 and 39. If one number is 3, calculate the other number.
Solution: Let the other number be k
We know that,
GCD × LCM = 3 × k
k = (GCD × LCM) / 3
k = (1 × 39) / 3
k = 13
Hence the other number is 13.
Frequently Asked Questions on LCM of 3 and 13
What is the LCM of 3 and 13?
Mention the difference between the LCM of 3 and 13 and the HCF of 3 and 13.
Name the methods used to find the LCM of 3 and 13.
The following methods are used to find the LCM of 3 and 13
Prime Factorisation
Division method
Listing the Multiples
How to determine the LCM of 3 and 13 using the prime factorisation method?
Here, we express the given numbers as the product of prime factors
3 = 3
13 = 13
LCM (3, 13) = 3 × 13 = 39
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