lcm of 9 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 13. The LCM is the smallest positive integer that is divisible by both 9 and 13, and this can be calculated using the prime factorization method or by listing the multiples of each number.
Answer
The least common multiple of 9 and 13 is $117$.
Answer for screen readers
The least common multiple (LCM) of 9 and 13 is 117.
Steps to Solve
- Identify the prime factors
First, we need to identify the prime factors of both numbers.
- The prime factorization of 9 is $3^2$ (since $9 = 3 \times 3$).
- The prime factorization of 13 is $13^1$ (since 13 is a prime number).
- Find the highest powers of each prime
Next, identify the highest powers of each prime factor involved in the factorization of both numbers.
- From 9, the prime factor 3 has the highest power of $3^2$.
- From 13, the prime factor 13 has the highest power of $13^1$.
- Multiply the highest powers of the prime factors
Now we will calculate the LCM by multiplying these highest powers together.
$$ LCM = 3^2 \times 13^1 $$
- Calculate the result
Finally, we compute the multiplication step:
$$ LCM = 9 \times 13 $$
Now calculate this final product:
$$ 9 \times 13 = 117 $$
The least common multiple (LCM) of 9 and 13 is 117.
More Information
The LCM helps to find a common multiple, which is especially useful in problems involving addition or subtraction of fractions with different denominators.
Tips
- Confusing the LCM with the greatest common divisor (GCD). Remember that LCM finds the smallest common multiple, while GCD finds the largest factor that divides both numbers.
- Forgetting to consider all prime factors. Ensure you include all prime bases with their highest powers.
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