The HCF and LCM of two numbers are 9 and 360, respectively. If one of the numbers is 45, what is the other number?

Step 1: Recall the relationship between HCF, LCM, and two numbers

For any two positive integers, the product of the numbers is always equal to the product of their Highest Common Factor (HCF) and Least Common Multiple (LCM). This is a fundamental property used to solve problems involving HCF and LCM.

Step 2: Identify the given values

From the problem statement, we are given the HCF as 9, the LCM as 360, and one of the two numbers as 45. We need to find the other number.

Step 3: Substitute the values into the formula

Now, we substitute the given values into the relationship we recalled in the first step. Let the 'Other number' be represented by a variable, say $x$. So, $45 \times x = 9 \times 360$.

Step 4: Calculate the product of HCF and LCM

First, we calculate the product of the HCF and LCM. Multiplying 9 by 360 gives us 3240.

Step 5: Solve for the other number

To find the other number, we divide the product of HCF and LCM (3240) by the given number (45). This calculation yields 72.

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