Find the HCF and LCM of
693, 1078

Answer

To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of the numbers 693 and 1078, we can follow these steps:

### Step 1: Find the HCF using the Division Method

1. **Divide the larger number by the smaller number**:
- Divide 1078 by 693.
- \( 1078 \div 693 = 1 \) (quotient) with a remainder of \( 1078 - 693 \times 1 = 385 \).

2. **Now, take the previous divisor (693) and divide it by the remainder (385)**:
- \( 693 \div 385 = 1 \) (quotient) with a remainder of \( 693 - 385 \times 1 = 308 \).

3. **Continue with the last divisor (385) and the new remainder (308)**:
- \( 385 \div 308 = 1 \) (quotient) with a remainder of \( 385 - 308 \times 1 = 77 \).

4. **Now divide the last divisor (308) by the new remainder (77)**:
- \( 308 \div 77 = 4 \) (quotient) with a remainder of \( 308 - 77 \times 4 = 0 \).

5. **Since the remainder is now 0, the last non-zero remainder is the HCF**:
- Thus, the HCF of 693 and 1078 is **77**.

### Step 2: Find the LCM using the relationship between HCF and LCM

1. **Use the formula**:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]
- Here, we have:
\[ 77 \times \text{LCM} = 693 \times 1078 \]

2. **Calculate the product of the two numbers**:
- \( 693 \times 1078 = 748734 \).

3. **Now, solve for LCM**:
\[ \text{LCM} = \frac{748734}{77} \]
- Performing the division:
- \( 748734 \div 77 = 9702 \).

4. **Thus, the LCM of 693 and 1078 is **9702**.

### Final Answer:
- HCF of 693 and 1078 is **77**.
- LCM of 693 and 1078 is **9702**.

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