What is the lowest common multiple of 5 and 9?
Understand the Problem
The question is asking for the lowest common multiple (LCM) of the numbers 5 and 9. This involves finding the smallest positive integer that is a multiple of both numbers.
Answer
45
Answer for screen readers
The final answer is 45
Steps to Solve
- Find the prime factorization of each number
The first step is to find the prime factorization of each number.
- The prime factorization of 5 is simply $5^1$ since 5 is a prime number.
- The prime factorization of 9 is $3^2$ since $9 = 3 \times 3$.
- Identify the highest power of each prime
Next, we identify the highest power of each prime number that appears in the factorizations.
- The primes are 5 (from 5) and 3 (from 9).
- The highest power of 5 is $5^1$.
- The highest power of 3 is $3^2$.
- Multiply the highest powers together
Finally, multiply these highest powers together to find the LCM.
$$LCM = 5^1 \times 3^2 = 5 \times 9 = 45$$
The final answer is 45
More Information
Interestingly, the LCM of 5 and 9 is simply the product of both numbers because they are relatively prime (they share no common factors other than 1).
Tips
A common mistake is to incorrectly calculate the prime factorization or to incorrectly multiply the prime factors together. To avoid this, double-check each prime factor and ensure they're correctly multiplied.
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