Find the LCM and HCF of 6 and 8

Options

A. 24,2
B. 12,2
C. 24,3
D. 8,6

Answer

To find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of 6 and 8, we can follow these steps:

### Step 1: Find the Prime Factorization
- **For 6**: The prime factors of 6 are \(2 \times 3\).
- **For 8**: The prime factors of 8 are \(2 \times 2 \times 2\) or \(2^3\).

### Step 2: Find the LCM
To find the LCM, we take the highest power of each prime factor that appears in the factorization of both numbers:
- The prime factor 2 appears in both numbers. The highest power of 2 is \(2^3\) (from 8).
- The prime factor 3 appears only in 6, and its highest power is \(3^1\).

Now, we multiply these together:
\[ \text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24 \]

### Step 3: Find the HCF
To find the HCF, we take the lowest power of each prime factor that appears in both numbers:
- The prime factor 2 appears in both numbers. The lowest power of 2 is \(2^1\) (from 6).
- The prime factor 3 does not appear in 8, so we do not consider it.

Now, we multiply these together:
\[ \text{HCF} = 2^1 = 2 \]

### Final Answers
- **LCM of 6 and 8**: 24
- **HCF of 6 and 8**: 2

### Summary
- LCM = 24
- HCF = 2