Question

lcm of 8 and 12

Answer 1

To find the least common multiple (LCM) of 8 and 12, you can use the prime factorization method or the formula involving the greatest common divisor (GCD). Here's how to do it using both methods:

### Method 1: Prime Factorization
1. Find the prime factorization of both numbers:
- 8 = \(2^3\)
- 12 = \(2^2 \times 3^1\)

2. Take the highest power of each prime factor:
- For 2: the highest power is \(2^3\)
- For 3: the highest power is \(3^1\)

3. Multiply these together to find the LCM:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]

### Method 2: Using GCD
1. First, find the GCD of 8 and 12, which is 4.

2. Use the LCM formula:
\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}
\]
where \(a = 8\) and \(b = 12\).

3. Substitute the values:
\[
\text{LCM}(8, 12) = \frac{8 \times 12}{4} = \frac{96}{4} = 24
\]

In both methods, we find that the LCM of 8 and 12 is **24**.