It is given that the HCF of two numbers is 72 and LCM of those two numbers is 4536. Both the numbers are greater than their HCF. Find the two numbers

Given that the Highest Common Factor (HCF) of two numbers is 72, and their Lowest Common Multiple (LCM) is 4536, we need to find the two numbers. 

Let the two numbers be \( a \) and \( b \).

We know that the product of the two numbers is equal to the product of their HCF and LCM:

\[
a \times b = \text{HCF} \times \text{LCM}
\]

Substituting the given values:

\[
a \times b = 72 \times 4536
\]

Let's calculate this:

\[
a \times b = 326592
\]

So, the product of the two numbers is 326592.

Now, we know that \( a = 72 \times x \) and \( b = 72 \times y \), where \( x \) and \( y \) are co-prime (since \( x \) and \( y \) will have no common factors other than 1). 

Then,

\[
72 \times

Learn how to find two numbers given their Highest Common Factor (HCF) and Lowest Common Multiple (LCM). In this problem, the HCF is 72, and the LCM is 4536. Follow a step-by-step solution including the calculation of the product of the numbers and the relationship between HCF, LCM, and the numbers themselves. Suitable for high school students.

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