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The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF is 1456. If one of the numbers is 160, then what is the other number?
  • a)
    120
  • b)
    136
  • c)
    144
  • d)
    184
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF ...
Understanding the Problem
To find the unknown number when one number is 160, we need to use the relationship between the HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers.
Key Relationships
- The relationship between LCM and HCF is given by:
LCM = HCF × (Product of the two numbers) / (HCF)^2
- According to the problem, we know:
- LCM = 90 × HCF
- LCM + HCF = 1456
This gives us two equations to work with.
Setting Up the Equations
1. Let HCF = h
2. Then, LCM = 90h
Substituting into the sum equation:
- 90h + h = 1456
- 91h = 1456
- h = 1456 / 91
- h = 16
Now we can find LCM:
- LCM = 90 × 16 = 1440
Using the HCF to Find the Other Number
We know the formula connecting LCM, HCF, and the two numbers:
- LCM = (Number1 × Number2) / HCF
Substituting the known values:
- 1440 = (160 × x) / 16
Solving for x (the unknown number)
- 1440 × 16 = 160 × x
- 23040 = 160 × x
- x = 23040 / 160
- x = 144
Thus, the other number is:
Conclusion
The other number is 144, confirming that the correct answer is option 'C'.
Free Test
Community Answer
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF ...
Let the HCF of 2 numbers be x.
Then, LCM of 2 numbers = 90x
According to the question,
LCM + HCF = 1456
90x + x = 1456
⇒ x = 16
HCF of 2 numbers = 16
LCM of 2 numbers = 1440
LCM × HCF = 1st number × 2nd number
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