Last updated on May 26th, 2025
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 .
The LCM of 13 and 15 is 195.
We find this using different methods which are explained below and apply it in different examples.
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;
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
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
In the division method,
Below are a few mistakes one is likely to make while learning to find the LCM of 13 and 15. Be mindful of the same while practicing.
a=13, b=15. Use LCM(a,b)=a×b/HCF(a,b) to find the LCM.
a=13, b=15.
HCF of 13,15;
Factors of the numbers;
13 = 1,13
15 = 1,3,5,15
HCF(13,15) = 1
Apply the formula
LCM(a,b)=a×b/HCF(a,b)
LCM(13,15)=13×15/1
LCM(13,15) = 195
By using LCM(a,b)=a×b/HCF(a,b) → the above is how we find the LCM of the numbers 13 and 15.
Verify a=13,b=15 LCM(a,b)×HCF(a,b)=a×b is satisfied.
LCM of 13,15 = 195
HCF of 13, 15 = 1
LCM(a,b)×HCF(a,b)=a×b
195×1 = 13×15
195 = 195
LHS = RHS, the relationship stands true.
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.
: She loves to read number jokes and games.