LCM of 3 and 13
2026-02-28 13:19 Diff
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Last updated on August 5, 2025

The least common multiple is the smallest common multiple of any number. Do you know how we use it in our daily life? We use LCM in our daily life to predict or schedule any events. In this article, Let’s check out some methods to calculate the LCM of 3 and 13

What is the LCM of 3 and 13

The LCM of 3 and 13 is 39. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways. 
 

How to find the LCM of 3 and 13

We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:


Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method


Now let us delve further into these three methods and how it benefits us.
 

LCM of 3 and 13 Using Listing the Multiples

In this method, we will list all the multiples of 3 and 13. Then we will try to find a multiple that is present in both numbers.

For example,

Multiples of 3: 3, 6, 9, ……, 30, 33, 39
Multiples of 13: 13, 26, 39, 52

The LCM of 3 and 13 is 39. 39 is the smallest number which can be divisible by both 3 and 13.
 

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LCM of 3 and 13 Using Prime Factorization

To find the LCM of 3 and 13 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM.

Prime Factors of 3 = 31
Prime Factors of 13 = 131

Multiply the highest power of both the factors: 31 × 131 = 39


Therefore, the LCM of 3 and 13 is 39.
 

LCM of 3 and 13 Using Division method

To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.

For finding the LCM of 3 and 13 we will use the following method.

By multiplying the prime divisors from the table, we will get the LCM of 3 and 13.
3 × 13 =39.


The LCM of 3 and 13 is 39.

Common Mistakes and How to Avoid Them in LCM of 3 and 13

Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
 

Problem 1

If Bob is planning to schedule his monthly activities. He wants to repeat one activity every 3 days and the other every 13 days. On which both activities will coincide?

Okay, lets begin

To find the day when activity coincides, we need to find the LCM of 3 and 13.


LCM of 3 and 3 = product of the highest power of the prime factors.


The prime factors of 3 = 31
The prime factor of 13 = 131
The LCM = 31 × 131 = 39
 

Explanation

So, at every 39 days, both the activities will coincide.
 

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Problem 2

At station A, the train arrives at every 13 mins and the bus at every 3 mins from 12 pm. So at which time both the train and bus are together?

Okay, lets begin

The train arrives the station at every 13 mins


The bus arrives the station at every 3 mins

The time the train and bus arrive together will be the LCM of 3 and 13

The LCM of 3 and 13 is 39. 
 

Explanation

Therefore, at 12:39 pm, both the bus and train come together.
 

Well explained 👍

Problem 3

Two professors take a lecture in the same classroom. One professor uses the classroom every 3 days and the other professor takes classes every 13days. How many days will it take both professors to use the classroom on the same day?

Okay, lets begin

The first professor takes class: 3 days


The second professor takes class: 13 days
 

Explanation

They both will end up taking class in the same classroom on the same day:3 x 13 = 39 days
 

Well explained 👍

Problem 4

Two events happen in cycles. One cycle happens every 3 days and the other cycle happens every 13 days. After how many days will both cycles occur on the same day?

Okay, lets begin

The first cycle takes place every: 3 days


The second cycle takes place every: 13 days
 

Explanation

So both cycles will occur on the same day in : 3 x 13 = 39 days
 

Well explained 👍

Problem 5

A mall hosts two events, the first event is held every 3 days and the second event is held every 13 days. If both events are happening at the same time today. Then after how many days will both events happen on the same day again?

Okay, lets begin

The first event happens every: 3 days


The second event happens every: 13 days

So both events will happen on the same day again after 3 x 13 = 39 days
 

Well explained 👍

FAQs on Least Common Multiple of 3 and 13.

1.What are the ways to calculate LCM?

There are different ways to calculate LCM, listing the multiples, prime factorization, and division methods are some common methods used to calculate the LCM.
 

2.List down the first five multiples of 3 and 13?

The first five multiples of 3 are 3, 6, 9, 12, 15
The first five multiples of 13 are 13, 26, 39, 52, 65
 

3.Calculate the LCM of 3 and 14?

Prime factors of 3 is 31
Prime factor of 14 is 21 × 71 
The LCM of 3 and 14 = 31 × 21 × 71
= 3 × 2 × 7 =42
The LCM of 3 and 14 is 42
 

Important Glossaries for LCM of 3 and 13

Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, only common factors are 1 and the number itself.


Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8 and 10. 


Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
 

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.