What is the least common multiple of 2 and 9?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 2 and 9, which involves finding the smallest number that is a multiple of both these numbers.
Answer
18
Answer for screen readers
The least common multiple of 2 and 9 is 18
Steps to Solve
- Prime Factorization of Each Number
Find the prime factorization of each number:
- The prime factorization of 2 is just 2.
- The prime factorization of 9 is $3^2$.
- Identify the Highest Power of Each Prime
Identify the highest power of each prime number involved:
- For the prime number 2, the highest power is $2^1$.
- For the prime number 3, the highest power is $3^2$.
- Multiply the Highest Powers of Each Prime
Multiply these highest powers together to find the LCM:
$$ \text{LCM} = 2^1 \times 3^2 = 2 \times 9 = 18 $$
The least common multiple of 2 and 9 is 18
More Information
The least common multiple (LCM) is the smallest number that is a multiple of both given numbers. It's useful in problems that involve adding or comparing fractions with different denominators.
Tips
A common mistake is to just multiply the numbers together without considering the highest powers of their prime factors. Always use the highest powers of all primes that appear in the factorization of either number.
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