What is the LCM of 15 and 13?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 15 and 13. The LCM is the smallest positive integer that is divisible by both numbers.
Answer
The least common multiple (LCM) is 195.
Answer for screen readers
The least common multiple (LCM) of 15 and 13 is 195.
Steps to Solve
-
Identify the Numbers The first step is to identify the two numbers for which we want to find the LCM. Here, the numbers are 15 and 13.
-
Check for Prime Factorization Since 15 and 13 are involved, we can analyze their prime factorizations:
- The prime factorization of 15 is $3 \times 5$.
- The prime factorization of 13 is $13$ (since it is a prime number).
- Find the LCM Using the Highest Powers of Prime Factors To find the LCM, we take each prime factor and use the highest power from each number:
- For 3, the highest power is $3^1$ (from 15).
- For 5, the highest power is $5^1$ (from 15).
- For 13, the highest power is $13^1$ (from 13).
Combining these gives us:
$$ \text{LCM} = 3^1 \times 5^1 \times 13^1 $$
- Calculate the LCM Now we compute the product:
$$ \text{LCM} = 3 \times 5 \times 13 $$
First, calculate $3 \times 5 = 15$.
Then, calculate $15 \times 13 = 195$.
So the LCM is 195.
The least common multiple (LCM) of 15 and 13 is 195.
More Information
The least common multiple is useful in problems involving multiple fractions or finding common denominators. It is the smallest number that both original numbers can divide without leaving a remainder.
Tips
- Confusing LCM with GCD (greatest common divisor) is a common mistake. Remember, LCM seeks to find a common multiple, while GCD finds a common divisor.
- Forgetting to multiply all prime factors together in their highest powers can lead to incorrect LCMs. Always ensure to take the highest power for each prime.
