least common multiple of 9 and 24
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 24. The LCM is the smallest positive integer that is divisible by both of these numbers. To find it, we can list the multiples of each number and identify the smallest common one.
Answer
72
Answer for screen readers
The least common multiple of 9 and 24 is 72
Steps to Solve
- Find the prime factorization of each number
Prime factorization is finding which prime numbers multiply together to make the original number.
$$9 = 3 imes 3 = 3^2$$
$$24 = 2 imes 2 imes 2 imes 3 = 2^3 imes 3$$
- Identify the highest power of each prime number
We need to take the highest power of all prime numbers that appear in the factorizations.
For 9 and 24, the prime numbers are 2 and 3.
Highest power of 2: $2^3$
Highest power of 3: $3^2$
- Multiply these highest powers together to find the LCM
$$\text{LCM} = 2^3 \times 3^2$$
Calculate it step-by-step:
$$2^3 = 8$$
$$3^2 = 9$$
$$8 \times 9 = 72$$
The least common multiple of 9 and 24 is 72
More Information
The LCM of two numbers can be found using their prime factorizations by taking the highest powers of all prime factors.
Tips
A common mistake is to incorrectly find the highest power of the prime factors. Make sure to identify all primes and compare their exponents correctly.
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