Find the HCF and LCM of
145, 232

Answer

To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of the numbers 145 and 232, we can follow these steps:

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

1. **Divide the larger number by the smaller number**:
- Divide 232 by 145.
- 232 ÷ 145 = 1 (remainder 87)
- So, we write: 232 = 145 × 1 + 87

2. **Now, take the previous divisor (145) and the remainder (87)**:
- Divide 145 by 87.
- 145 ÷ 87 = 1 (remainder 58)
- So, we write: 145 = 87 × 1 + 58

3. **Now, take the previous divisor (87) and the remainder (58)**:
- Divide 87 by 58.
- 87 ÷ 58 = 1 (remainder 29)
- So, we write: 87 = 58 × 1 + 29

4. **Now, take the previous divisor (58) and the remainder (29)**:
- Divide 58 by 29.
- 58 ÷ 29 = 2 (remainder 0)
- So, we write: 58 = 29 × 2 + 0

5. **Since the remainder is now 0**, the last non-zero remainder (29) is the HCF.
- Therefore, HCF(145, 232) = 29.

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

The relationship between HCF and LCM is given by the formula:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

1. **Calculate the product of the two numbers**:
- Product = 145 × 232 = 33640.

2. **Now, use the HCF we found**:
- HCF = 29.

3. **Substituting into the formula**:
\[ 29 \times \text{LCM} = 33640 \]

4. **Now, solve for LCM**:
\[ \text{LCM} = \frac{33640}{29} = 1160 \]

### Final Answers:
- HCF(145, 232) = 29
- LCM(145, 232) = 1160

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