Find LCM and HCF of 0.6, 1.8 and 0.36.

Answer

To find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the numbers 0.6, 1.8, and 0.36, we can follow these steps:

### Step 1: Convert the decimal numbers to fractions
- **0.6** can be written as \( \frac{6}{10} \)
- **1.8** can be written as \( \frac{18}{10} \)
- **0.36** can be written as \( \frac{36}{100} \)

### Step 2: Simplify the fractions
- \( \frac{6}{10} = \frac{3}{5} \) (dividing both numerator and denominator by 2)
- \( \frac{18}{10} = \frac{9}{5} \) (dividing both numerator and denominator by 2)
- \( \frac{36}{100} = \frac{18}{50} = \frac{9}{25} \) (dividing both numerator and denominator by 2)

So, the fractions are:
- \( \frac{3}{5} \)
- \( \frac{9}{5} \)
- \( \frac{9}{25} \)

### Step 3: Find the LCM of the numerators
The numerators are 3, 9, and 9. The LCM of these numbers:
- The multiples of 3: 3, 6, 9, 12, 15, 18, ...
- The multiples of 9: 9, 18, 27, ...
- The least common multiple is **9**.

### Step 4: Find the HCF of the denominators
The denominators are 5, 5, and 25. The HCF of these numbers:
- The factors of 5: 1, 5
- The factors of 25: 1, 5, 25
- The highest common factor is **5**.

### Step 5: Calculate LCM and HCF of the fractions
- **LCM** of the fractions \( \frac{3}{5}, \frac{9}{5}, \frac{9}{25} \):
\[ \text{LCM} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} = \frac{9}{5} \]

- **HCF** of the fractions \( \frac{3}{5}, \frac{9}{5}, \frac{9}{25} \):
\[ \text{HCF} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{3}{25} \]

### Step 6: Convert back to decimal form
- LCM: \( \frac{9}{5} = 1.8 \)
- HCF: \( \frac{3}{25} = 0.12 \)

### Final Answers
- **LCM**: 1.8
- **HCF**: 0.12