lcm of 8 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 8 and 13. To find the LCM, we can use the formula that involves finding the prime factors of both numbers or using the formula LCM(a, b) = (a * b) / GCD(a, b), where GCD is the greatest common divisor.
Answer
$104$
Answer for screen readers
The least common multiple (LCM) of 8 and 13 is $104$.
Steps to Solve

Identify the Numbers We are finding the LCM of two numbers: 8 and 13.

Calculate the GCD The greatest common divisor (GCD) of 8 and 13 can be found. Since 8 is made up of the prime factor $2^3$, and 13 is prime, the GCD is 1. $$ \text{GCD}(8, 13) = 1 $$

Use the LCM Formula We apply the formula to find the LCM using the GCD. $$ \text{LCM}(8, 13) = \frac{8 \times 13}{\text{GCD}(8, 13)} $$

Perform the Calculation Now, we compute: $$ \text{LCM}(8, 13) = \frac{8 \times 13}{1} = 104 $$
The least common multiple (LCM) of 8 and 13 is $104$.
More Information
The LCM of two numbers is the smallest multiple that both numbers share. In this case, since 13 is a prime number and does not share any factors with 8, the LCM is simply the product of the two numbers. The numbers 8 and 13 can be used in various applications, such as arranging items in groups or finding synchronization in cycles.
Tips
 A common mistake is miscalculating the GCD. Remember, if the numbers have no common factors other than 1, the GCD is 1.
 Another mistake is directly multiplying the two numbers without considering the GCD, which would lead to confusion.