What is the LCM of 9 and 24?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 9 and 24. To find the LCM, we typically identify the prime factors of each number and then take the highest power of each prime factor involved.
Answer
$72$
Answer for screen readers
The least common multiple of 9 and 24 is $72$.
Steps to Solve
- Identify the prime factors of each number
For the number 9, we have: $$ 9 = 3^2 $$
For the number 24, the prime factorization is: $$ 24 = 2^3 \cdot 3^1 $$
- List all prime factors with their highest powers
From the factorizations, we note the following prime factors and their highest powers:
- The prime factor 2 appears as $2^3$ (from 24).
- The prime factor 3 appears as $3^2$ (from 9).
- Multiply the highest powers of each prime factor
To find the LCM, we multiply the highest powers identified: $$ \text{LCM} = 2^3 \cdot 3^2 $$
Calculating this gives: $$ \text{LCM} = 8 \cdot 9 $$
- Calculate the final value
Now, perform the multiplication: $$ 8 \cdot 9 = 72 $$
Therefore, the least common multiple of 9 and 24 is 72.
The least common multiple of 9 and 24 is $72$.
More Information
The least common multiple is a key concept in number theory and is often used in various mathematical calculations involving fractions, ratios, and scheduling problems.
Tips
- A common mistake is forgetting to take the highest power of each prime factor. Always check to ensure you include the maximum exponent for every prime from the factorization of both numbers.
