If the LCM and HCF of two numbers are 78 and 13 respectively, the product of two numbers can be expressed as:Options 2x3x13x11 2x3x13x12 2x3x13x13 2x3x13x14

1. Break Down the Problem

We are given the Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two numbers. We want to find the product of those two numbers using the relationship between LCM, HCF, and the product of two numbers.

2. Relevant Concepts

The relationship between the LCM, HCF, and the two numbers $a$ and $b$ is given by the formula: $a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b)$

In this case, we have:

• LCM = 78
• HCF = 13

3. Analysis and Detail

Using the formula, we can substitute the known values: $a \times b = 78 \times 13$

4. Verify and Summarize

Calculating the product: $78 \times 13 = 1014$

Final Answer

Thus, the product of the two numbers can be expressed as $1014$. Since we need to express $1014$ in one of the provided options, we can factor $1014$ as: $1014 = 2 \times 3 \times 13 \times 13$ This corresponds to the option $2 \times 3 \times 13 \times 13$.

Therefore, the answer is: $2 \times 3 \times 13 \times 13$.