Find the HCF and LCM of
234, 572

Answer

To find the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the numbers 234 and 572, we can follow these steps:

### Step 1: Find the HCF using the Division Method
1. **Divide the larger number by the smaller number**:
- Divide 572 by 234.
- Calculate: \( 572 \div 234 = 2 \) (quotient) with a remainder.
- Remainder = \( 572 - (234 \times 2) = 572 - 468 = 104 \).

2. **Repeat the process**:
- Now, divide 234 by the remainder 104.
- Calculate: \( 234 \div 104 = 2 \) (quotient) with a remainder.
- Remainder = \( 234 - (104 \times 2) = 234 - 208 = 26 \).

3. **Continue dividing**:
- Now, divide 104 by the new remainder 26.
- Calculate: \( 104 \div 26 = 4 \) (quotient) with a remainder.
- Remainder = \( 104 - (26 \times 4) = 104 - 104 = 0 \).

4. **Identify the HCF**:
- When the remainder becomes 0, the last divisor used is the HCF.
- Thus, HCF(234, 572) = 26.

### Step 2: Find the LCM using the relationship between HCF and LCM
1. **Use the formula**:
- The relationship between HCF and LCM is given by:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]
- Therefore, we can rearrange this to find the LCM:
\[ \text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}} \]

2. **Calculate the product of the two numbers**:
- Product = \( 234 \times 572 \).

3. **Calculate the LCM**:
- LCM = \( \frac{234 \times 572}{26} \).
- First, calculate \( 234 \times 572 = 134568 \).
- Now divide by the HCF: \( \frac{134568}{26} = 5172 \).

### Final Results:
- HCF(234, 572) = 26
- LCM(234, 572) = 5172

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