Find the HCF and LCM of
861,`" "` 1353

Options

A. 113,`" "` 9471
B. 123,`" "` 9471
C. 123,`" "` 9441
D. 103,`" "` 9471

Answer

To find the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of the numbers 861 and 1353, we will follow these steps:

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

1. **Divide the larger number by the smaller number**:
- Divide 1353 by 861.
- 1353 ÷ 861 = 1 (remainder 492)
- So, we write: 1353 = 861 × 1 + 492

2. **Now, take the divisor (861) and the remainder (492)**:
- Divide 861 by 492.
- 861 ÷ 492 = 1 (remainder 369)
- So, we write: 861 = 492 × 1 + 369

3. **Repeat the process**:
- Divide 492 by 369.
- 492 ÷ 369 = 1 (remainder 123)
- So, we write: 492 = 369 × 1 + 123

4. **Continue until the remainder is 0**:
- Divide 369 by 123.
- 369 ÷ 123 = 3 (remainder 0)
- So, we write: 369 = 123 × 3 + 0

5. **The last non-zero remainder is the HCF**:
- Therefore, HCF(861, 1353) = 123.

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

1. **Use the formula**:
- HCF × LCM = Product of the two numbers.
- HCF(861, 1353) × LCM(861, 1353) = 861 × 1353.

2. **Calculate the product of the two numbers**:
- 861 × 1353 = 116,1933.

3. **Now, substitute the HCF into the formula**:
- 123 × LCM = 116,1933.

4. **Solve for LCM**:
- LCM = 116,1933 ÷ 123 = 9471.

### Final Results:
- HCF of 861 and 1353 is **123**.
- LCM of 861 and 1353 is **9471**.

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