Find the HCF and LCM of 3,6,24 and 12

Answer

To find the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the numbers 3, 6, 24, and 12, we can follow these steps:

### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.

- **3**: The prime factorization of 3 is \(3^1\).
- **6**: The prime factorization of 6 is \(2^1 \times 3^1\).
- **24**: The prime factorization of 24 is \(2^3 \times 3^1\).
- **12**: The prime factorization of 12 is \(2^2 \times 3^1\).

### Step 2: Finding the HCF
To find the HCF, we take the lowest power of all prime factors that appear in each of the numbers.

- The common prime factors are:
- For \(2\): The lowest power is \(2^0\) (since 3 does not have 2 as a factor).
- For \(3\): The lowest power is \(3^1\).

Thus, the HCF is:
\[ HCF = 2^0 \times 3^1 = 1 \times 3 = 3 \]

### Step 3: Finding the LCM
To find the LCM, we take the highest power of all prime factors that appear in any of the numbers.

- The prime factors and their highest powers are:
- For \(2\): The highest power is \(2^3\) (from 24).
- For \(3\): The highest power is \(3^1\).

Thus, the LCM is:
\[ LCM = 2^3 \times 3^1 = 8 \times 3 = 24 \]

### Final Result
- HCF of 3, 6, 24, and 12 is **3**.
- LCM of 3, 6, 24, and 12 is **24**.

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