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
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Identify the Numbers We are finding the LCM of two numbers: 8 and 13.
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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. $$ \text{GCD}(8, 13) = 1 $$
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Use the LCM Formula We apply the formula to find the LCM using the GCD. $$ \text{LCM}(8, 13) = \frac{8 \times 13}{\text{GCD}(8, 13)} $$
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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.
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