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The sum of LCM and HCF of two numbers is 4956. Those numbers are in the ratio of 11:16. What is the difference of LCM and HCF of two numbers? The options are 4480, 4620, 4780, and 4900.
please help me to solve this question?
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The sum of LCM and HCF of two numbers is 4956. Those numbers are in th...
Understanding the Problem
The problem states that the sum of the LCM (Least Common Multiple) and HCF (Highest Common Factor) of two numbers is 4956, and these numbers are in the ratio of 11:16. We need to find the difference between the LCM and HCF.
Step 1: Ratio Representation
Let the two numbers be represented as:
- Number 1: 11x
- Number 2: 16x
Step 2: Formulas for LCM and HCF
For any two numbers a and b:
- HCF(a, b) = k (where k is the HCF)
- LCM(a, b) = (a * b) / HCF(a, b)
Thus, for our numbers:
- HCF(11x, 16x) = x (since HCF is based on the common factor)
- LCM(11x, 16x) = (11x * 16x) / x = 176x
Step 3: Equation Setup
According to the problem:
- LCM + HCF = 4956
- Therefore, 176x + x = 4956
- This simplifies to 177x = 4956
Step 4: Solve for x
From the equation, we can find x:
- x = 4956 / 177
- x = 28
Step 5: Calculate LCM and HCF
Now, substitute the value of x back:
- HCF = x = 28
- LCM = 176x = 176 * 28 = 4928
Step 6: Find the Difference
Finally, calculate the difference between LCM and HCF:
- Difference = LCM - HCF = 4928 - 28 = 4900
Conclusion
The difference between the LCM and the HCF of the two numbers is 4900.
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The sum of LCM and HCF of two numbers is 4956. Those numbers are in the ratio of 11:16. What is the difference of LCM and HCF of two numbers? The options are 4480, 4620, 4780, and 4900.please help me to solve this question?
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