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184 LearnersLast updated on November 30th, 2024
LCM of 13 and 15
We use the LCM in basic everyday operations like making music and setting alarms. LCM of 13 and 15 is the smallest positive integer that divides the numbers with no numbers left behind. In this article, lets learn more about the LCM .
What is the LCM of 13 and 15?
The LCM of 13 and 15 is 195.
We find this using different methods which are explained below and apply it in different examples.
How to find the LCM of 13 and 15?
The LCM of 13 and 15 can be found using the listing multiples method, the prime factorization method and the division method. These are explained below;
Listing multiples method
In this method, we just list down the multiples of both the numbers till we land at the smallest common number between the digits.
To illustrate;
Multiples of 13 = 13,26,39,52,65,78,91,104,117,130…195
Multiples of 15 = 15,30,45,60,75,90,105,…195
From the above we can tell that the smallest number, common among 13 and 15 is 195.
LCM(13,15) = 195
Prime factorization method
Here, we factorize the numbers into their prime factors and multiply the highest powers to find the LCM. In the case of 13 and 15;
Step 1: Prime factorize,
13 = 13
15 = 3×5
Step 2: Multiply the highest powers,
LCM of 13 and 15 = 13×3×5
Step 3: Multiply the factors to get the LCM
LCM(13,15) = 195
Division method
In the division method,
- Write the numbers given (13,15) in a row.
- Proceed with dividing the numbers with a factor that id divisible by at least one of the numbers.
- Carry forward the numbers that are not divided earlier.
- Continue division till the remainder is 1.
- Multiply the divisors in the first column to find the LCM.
- LCM(13,15) = 195
Common mistakes and How to avoid them in the LCM of 13 and 15
LCM of 13 and 15 Examples
Problem 1
a=13, b=15. Use LCM(a,b)=a×b/HCF(a,b) to find the LCM.
Explanation
Problem 2
Verify a=13,b=15 LCM(a,b)×HCF(a,b)=a×b is satisfied.
Explanation
FAQs on the LCM of 13 and 15
1.What is the LCM of 3 and 15?
2.What is the LCM of 2 and 15?
3.What is the LCM of 15 and 75?
4.Find the HCF of 8 and 24.
5.What is the LCM of 16 and 24?
Important glossaries for the LCM of 13 and 15
- Multiple : It is a product of a number and any natural integer. So for 18; 18,36,54 are the multiples.
- Prime Factor : It is a prime number that one gets after factorization of any given number. Like for 15; 1,3,5, and 15 are prime factors as they can be divided by 1 or the number itself.
- Prime Factorization : It is a process of dividing the number into prime factors.
- Co-prime numbers : These are the positive integers, where both the numbers can be divided only by 1.
- Fraction : It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 13/15 , 13 is the numerator and 15 is the denominator. Proper fraction is where numerator is always lesser than denominator.
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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.
