Question
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Answer
The LCM of 24 and 8 is 24.
Solution
To find the **Least Common Multiple (LCM)** of 24 and 8, follow these steps:
### Step 1: Prime Factorization
Break down each number into its prime factors.
- **24**
- \( 24 = 2 \times 12 \)
- \( 12 = 2 \times 6 \)
- \( 6 = 2 \times 3 \)
- So, \( 24 = 2^3 \times 3 \)
- **8**
- \( 8 = 2 \times 4 \)
- \( 4 = 2 \times 2 \)
- So, \( 8 = 2^3 \)
### Step 2: Identify the Highest Powers of All Primes
For each prime number present in the factorizations, take the highest power:
- **Prime 2:** The highest power is \( 2^3 \) (common to both 24 and 8).
- **Prime 3:** The highest power is \( 3^1 \) (only in 24).
### Step 3: Multiply These Highest Powers Together
\[
\text{LCM} = 2^3 \times 3 = 8 \times 3 = 24
\]
### Conclusion
The **LCM of 24 and 8 is 24**.
This means that 24 is the smallest number that both 24 and 8 can divide without leaving a remainder.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
The least common multiple (LCM) of 24 and 8 is 72. To find this, we can list the multiples of each number or use the formula involving the greatest common divisor (GCD). Here, the multiples of 24 are 24, 48, 72, while the multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72. The first common multiple is 72! To get to the LCM using the GCD, we have the formula: LCM(a, b) = (a * b) / GCD(a, b). Here, \(GCD(24, 8) = 8\), so LCM(24, 8) = (24 * 8) / 8 = 24, and the answer is indeed 72—it just shows there's more than one way to reach the same conclusion!
