The product of LCM and HCF of `(2)/(3) and (3)/(5)` is

Options

A. `(2)/(5)`
B. `(5)/(2)`
C. `(3)/(5)`
D. `(5)/(3)`

Answer

To solve the problem of finding the product of the LCM and HCF of the fractions \( \frac{2}{3} \) and \( \frac{3}{5} \), we can follow these steps:

### Step 1: Understand the relationship between LCM and HCF
The relationship between the LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers \( a \) and \( b \) is given by the formula:
\[ \text{LCM} \times \text{HCF} = a \times b \]
In our case, \( a = \frac{2}{3} \) and \( b = \frac{3}{5} \).

### Step 2: Calculate the product of the two fractions
We need to calculate:
\[ a \times b = \frac{2}{3} \times \frac{3}{5} \]
To multiply these fractions, we multiply the numerators and the denominators:
\[ = \frac{2 \times 3}{3 \times 5} = \frac{6}{15} \]

### Step 3: Simplify the product
Now, we simplify \( \frac{6}{15} \):
\[ \frac{6}{15} = \frac{2}{5} \quad \text{(by dividing both numerator and denominator by 3)} \]

### Step 4: Conclusion
According to the relationship between LCM and HCF:
\[ \text{LCM} \times \text{HCF} = \frac{2}{5} \]
Thus, the product of the LCM and HCF of \( \frac{2}{3} \) and \( \frac{3}{5} \) is \( \frac{2}{5} \).

### Final Answer
The product of LCM and HCF of \( \frac{2}{3} \) and \( \frac{3}{5} \) is \( \frac{2}{5} \).

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