If HCF(P, 8) = 4 and LCM(P, 8) = 24, then the value of P is?

Understand the Problem

The question asks for the value of P given the HCF and LCM of P and 8. It involves using the relationship between HCF, LCM, and the numbers involved.

Answer

The value of $P$ is $ 12 $.

Steps to Solve

Understanding HCF and LCM Relationship

The relationship between two numbers and their Highest Common Factor (HCF) and Lowest Common Multiple (LCM) is given by the formula:

$$ HCF \times LCM = \text{Product of the two numbers} $$

Here, we have $HCF(P, 8) = 4$ and $LCM(P, 8) = 24$.

Using the formula

Substituting the known values into the formula:

$$ 4 \times 24 = P \times 8 $$

Calculating the left side

Now calculate the left side:

$$ 4 \times 24 = 96 $$

Thus, we have:

$$ 96 = P \times 8 $$

Solving for P

Now, we divide both sides by 8 to solve for $P$:

$$ P = \frac{96}{8} $$

Final Calculation

Calculating the right side:

$$ P = 12 $$

The value of $P$ is ( 12 ).

More Information

The relationship between HCF and LCM is fundamental in number theory. It allows us to connect properties of two numbers to their factors and multiples.

Tips

Confusing the HCF and LCM: It's essential to understand the definitions. HCF is the largest factor common to both numbers, while LCM is the smallest multiple common to both.
Incorrectly applying the formula: Ensure to multiply HCF and LCM correctly before equating to the product of the numbers.

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