What is the LCM of 24 and 9?
Understand the Problem
The question is asking for the least common multiple (LCM) of the two numbers, 24 and 9. To find the LCM, we will determine the smallest multiple that both numbers share.
Answer
The LCM of 24 and 9 is $72$.
Answer for screen readers
The least common multiple (LCM) of 24 and 9 is $72$.
Steps to Solve
- Find the prime factorization of each number
Start by breaking down 24 and 9 into their prime factors. For 24: $$ 24 = 2^3 \times 3^1 $$ For 9: $$ 9 = 3^2 $$
- Identify the highest powers of each prime factor
Next, identify the highest power of each prime factor found in either factorization. From 24:
- $2^3$ (highest power of 2)
- $3^1$ (from 24)
From 9:
- $3^2$ (highest power of 3)
The highest powers are:
- $2^3$
- $3^2$
- Multiply the highest powers together
Now, multiply these highest powers together to find the LCM. $$ LCM = 2^3 \times 3^2 $$
- Calculate the final result
Now, calculate the multiplication.
- First, $2^3 = 8$
- Then, $3^2 = 9$ Now multiply these together: $$ LCM = 8 \times 9 = 72 $$
The least common multiple (LCM) of 24 and 9 is $72$.
More Information
The least common multiple (LCM) is useful in various fields such as finding common denominators in fractions. In this case, $72$ is the smallest number that both 24 and 9 can divide into without leaving a remainder.
Tips
- Forgetting to consider all prime factors from both numbers.
- Not taking the highest power of each prime factor.
- Confusing LCM with GCD (Greatest Common Divisor).
