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154 LearnersLast updated on December 24th, 2024
LCM of 3 and 13
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.
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
LCM of 3 and 13 examples
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
FAQs on Least Common Multiple of 3 and 13.
1.What are the ways to calculate LCM?
2.List down the first five multiples of 3 and 13?
3.Calculate the LCM of 3 and 14?
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.
