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. 
 

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, 

• 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

• 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.