Find the HCF and LCM of `4/(5),6/(11),3/(5)`.

Answer

To find the HCF and LCM of the fractions \( \frac{4}{5}, \frac{6}{11}, \frac{3}{5} \), we will follow the steps outlined below.

### Step 1: Finding the HCF of the Numerators
First, we need to find the HCF (Highest Common Factor) of the numerators: 4, 6, and 3.

- The factors of 4 are: 1, 2, 4
- The factors of 6 are: 1, 2, 3, 6
- The factors of 3 are: 1, 3

The common factors are: 1. Therefore, the HCF of 4, 6, and 3 is **1**.

### Step 2: Finding the LCM of the Denominators
Next, we find the LCM (Lowest Common Multiple) of the denominators: 5, 11, and 5.

- The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, ...
- The multiples of 11 are: 11, 22, 33, 44, 55, ...

The smallest common multiple is **55**. Therefore, the LCM of 5, 11, and 5 is **55**.

### Step 3: Finding the HCF of the Fractions
Now, we can find the HCF of the fractions using the formula:
\[ \text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{1}{55} \]

### Step 4: Finding the LCM of the Numerators
Next, we find the LCM of the numerators: 4, 6, and 3.

- The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
- The multiples of 6 are: 6, 12, 18, 24, ...
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, ...

The smallest common multiple is **12**. Therefore, the LCM of 4, 6, and 3 is **12**.

### Step 5: Finding the HCF of the Denominators
Finally, we find the HCF of the denominators: 5, 11, and 5.

- The factors of 5 are: 1, 5
- The factors of 11 are: 1, 11

The only common factor is **1**. Therefore, the HCF of 5, 11, and 5 is **1**.

### Step 6: Finding the LCM of the Fractions
Now, we can find the LCM of the fractions using the formula:
\[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} = \frac{12}{1} = 12 \]

### Final Answers
- HCF of the fractions \( \frac{4}{5}, \frac{6}{11}, \frac{3}{5} \) is \( \frac{1}{55} \).
- LCM of the fractions \( \frac{4}{5}, \frac{6}{11}, \frac{3}{5} \) is \( 12 \).