दो संख्याओं के HCF और LCM का गुणनफल 3364 है तथा उनमें से एक संख्या 116 है तो दूसरी संख्या का मान बताएं। दो संख्याओं के HCF और LCM का गुणनफल 3364 है तथा उनमें से एक संख्या 116 है तो दूसरी संख्या का मान बताएं।
Understand the Problem
प्रश्न दो संख्याओं के HCF और LCM के गुणनफल से संबंधित है, और यह पूछता है कि यदि इन संख्याओं में से एक संख्या 116 है, तो दूसरी संख्या क्या होगी।
Answer
The second number is \( 29 \).
Answer for screen readers
The second number is ( 29 ).
Steps to Solve
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Understand the relationship between HCF, LCM, and the product of two numbers The product of the HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two numbers equals the product of the numbers themselves. So, if we denote the first number as $a$ (which is 116) and the second number as $b$, we have: $$ HCF(a, b) \times LCM(a, b) = a \times b $$
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Identify what we know We know:
- ( a = 116 )
- ( HCF(a, b) \times LCM(a, b) = 3364 )
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Set up the equation From the relationship stated above, we can write: $$ HCF(116, b) \times LCM(116, b) = 3364 $$
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Calculate the second number Since ( a \times b = 3364 ): $$ 116 \times b = 3364 $$
To find $b$, rearrange to isolate $b$: $$ b = \frac{3364}{116} $$
- Perform the division Now, calculate the value of $b$: $$ b = \frac{3364}{116} = 29 $$
The second number is ( 29 ).
More Information
In this problem, we utilized the relationship between HCF and LCM to find the second number. The product of the two numbers (116 and the unknown) equaled 3364, allowing us to derive the value.
Tips
- Confusing HCF and LCM: Some may confuse HCF and LCM while using their product. Always ensure you understand which is which.
- Division errors: Ensure proper division when calculating the second number from the equation.
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