What is the LCM of 13 and 5?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 13 and 5. To find the LCM, we can use the formula that the LCM of two numbers is the product of the numbers divided by their greatest common divisor (GCD). Since 13 and 5 are both prime numbers, their GCD is 1, leading to the calculation LCM(13, 5) = (13 * 5) / 1.
Answer
The LCM of 13 and 5 is $65$.
Answer for screen readers
The least common multiple (LCM) of 13 and 5 is 65.
Steps to Solve
-
Identify the numbers and their GCD
We have the numbers 13 and 5. Since both are prime numbers, their greatest common divisor (GCD) is 1. -
Apply the LCM formula
The formula to find the least common multiple (LCM) is: $$ \text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)} $$ Substituting in our numbers: $$ \text{LCM}(13, 5) = \frac{13 \times 5}{\text{GCD}(13, 5)} $$ -
Calculate the product of the numbers
Now we calculate the product of 13 and 5: $$ 13 \times 5 = 65 $$ -
Divide by the GCD to find LCM
Using the GCD we identified earlier, which is 1: $$ \text{LCM}(13, 5) = \frac{65}{1} = 65 $$
The least common multiple (LCM) of 13 and 5 is 65.
More Information
The LCM is the smallest number that is a multiple of both original numbers. In this case, 65 is the smallest number that can be divided evenly by both 13 and 5. Prime numbers always have an LCM that is simply their product since their GCD is always 1.
Tips
- Mixing up GCD and LCM: It's important to remember that GCD is used in the LCM formula, and confusing the two can lead to incorrect calculations. Be sure to find the GCD first before applying the formula.
