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CAT Exam  >  CAT Questions  >   The LCM of two numbers is 90 times their HCF... Start Learning for Free
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF is 1456 . If one of the number 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?
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Verified Answer
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF ...
Let the HCF of two numbers be x.
∴ LCM of two numbers be 90x.
According to the question,
∴ HCF of two numbers =16
and LCM of two numbers =90×16
= 1440
We know that, LCM ×HCF= Product of two numbers
⇒ 1440 x 16 = 160 x second number
Hence, the correct option is (C).
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Most Upvoted Answer
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF ...
Given:
LCM = 90 times HCF
LCM + HCF = 1456
One number = 160

To find:
The other number

Let's assume the other number to be x.

We know that LCM = (Number 1 * Number 2) / HCF

Given that LCM = 90 times HCF, we can write the equation as:
(Number 1 * Number 2) / HCF = 90 * HCF

Cross-multiplying, we get:
(Number 1 * Number 2) = 90 * (HCF)^2

We also know that LCM + HCF = 1456
Substituting the values of LCM and HCF, we get:
(Number 1 * Number 2) / HCF + HCF = 1456

Substituting the value of LCM from the previous equation, we get:
(90 * (HCF)^2) / HCF + HCF = 1456

Simplifying the equation, we get:
90 * HCF + HCF^2 = 1456 * HCF

Rearranging the terms, we get:
HCF^2 - 1456 * HCF + 90 * HCF = 0

Simplifying the equation further, we get:
HCF^2 - 1366 * HCF = 0

Factoring out HCF, we get:
HCF * (HCF - 1366) = 0

Since HCF cannot be zero, we have:
HCF - 1366 = 0

Solving for HCF, we get:
HCF = 1366

Now, we can find the LCM using the equation:
LCM = (Number 1 * Number 2) / HCF

Substituting the values, we get:
LCM = (160 * x) / 1366

Given that LCM + HCF = 1456, we can write the equation as:
(160 * x) / 1366 + 1366 = 1456

Simplifying the equation, we get:
160 * x + 1366 * 1366 = 1456 * 1366

Rearranging the terms, we get:
160 * x = 1456 * 1366 - 1366 * 1366

Simplifying further, we get:
160 * x = 1366 * (1456 - 1366)

Dividing both sides by 160, we get:
x = (1366 * 90) / 160

Simplifying the equation, we get:
x = 1366 * 9 / 16
x = 765.1875

Since the other number must be a whole number, the closest option is 144 (option C).

Therefore, the other number is 144.
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Community Answer
The LCM of two numbers is 90 times their HCF. The sum of LCM and HCF ...
Let the HCF of two numbers be x.
∴ LCM of two numbers be 90x.
According to the question,
∴ HCF of two numbers =16
and LCM of two numbers =90×16
= 1440
We know that, LCM ×HCF= Product of two numbers
⇒ 1440 x 16 = 160 x second number
Hence, the correct option is (C).
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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 number is 160 , then what is the other number?a)120b)136c)144d)184Correct answer is option 'C'. Can you explain this answer?
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