Question
Using the factor method find the lcm of 16&18
Answers
GPT-4o mini
To find the least common multiple (LCM) of 16 and 18 using the factor method, we first need to determine the prime factorization of each number.
**Step 1: Prime Factorization**
- **16**:
\[
16 = 2^4
\]
- **18**:
\[
18 = 2^1 \times 3^2
\]
**Step 2: Identify the highest power of each prime factor**
- For the prime number **2**, the highest power from the factorizations is \(2^4\) (from 16).
- For the prime number **3**, the highest power is \(3^2\) (from 18).
**Step 3: Multiply the highest powers together**
Now, we multiply the highest powers of each prime factor to find the LCM:
\[
\text{LCM} = 2^4 \times 3^2
\]
**Step 4: Calculate the LCM**
Calculating this gives:
\[
= 16 \times 9 = 144
\]
Therefore, the least common multiple (LCM) of 16 and 18 is **144**.
**Step 1: Prime Factorization**
- **16**:
\[
16 = 2^4
\]
- **18**:
\[
18 = 2^1 \times 3^2
\]
**Step 2: Identify the highest power of each prime factor**
- For the prime number **2**, the highest power from the factorizations is \(2^4\) (from 16).
- For the prime number **3**, the highest power is \(3^2\) (from 18).
**Step 3: Multiply the highest powers together**
Now, we multiply the highest powers of each prime factor to find the LCM:
\[
\text{LCM} = 2^4 \times 3^2
\]
**Step 4: Calculate the LCM**
Calculating this gives:
\[
= 16 \times 9 = 144
\]
Therefore, the least common multiple (LCM) of 16 and 18 is **144**.