The HCF and LCM of two numbers are 11 and 770, respectively. If one of the numbers is 45, what is the other number?
Answer: The other number is approximately 188.22. However, since HCF and LCM are defined for integers, and the result is not an integer, there might be an error in the problem statement's given values.
Step-by-step solution
Step 1: Recall the relationship between HCF, LCM, and two numbers
For any two positive integers, the product of their Highest Common Factor (HCF) and Least Common Multiple (LCM) is always equal to the product of the numbers themselves. This is a fundamental property in number theory.
Step 2: Substitute the given values into the formula
We are given the HCF as 11, the LCM as 770, and one of the numbers as 45. We substitute these values into the formula to set up an equation to find the other number.
Step 3: Calculate the product of HCF and LCM
First, we multiply the HCF (11) by the LCM (770) to find their product. This gives us 8470.
Step 4: Solve for the other number
To find the other number, we need to isolate it. We do this by dividing the product of the HCF and LCM (8470) by the given number (45).
Step 5: Perform the division
Upon performing the division, we find that the other number is approximately 188.22. However, HCF and LCM are defined for integers, implying the numbers themselves should be integers. Since 8470 is not perfectly divisible by 45, this indicates that the problem statement might contain an error, as the HCF and LCM property holds true only for integers.
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