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Airforce X Y / Indian Navy SSR Exam  >  Airforce X Y / Indian Navy SSR Questions  >  The LCM of two numbers is 14 times their HCF.... Start Learning for Free
The LCM of two numbers is 14 times their HCF. If one of the numbers is 36 and the sum of the LCM and the HCF is 270, then the other number is:
  • a)
    126
  • b)
    144
  • c)
    252
  • d)
    234
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The LCM of two numbers is 14 times their HCF. If one of the numbers is...
Given:
LCM of two numbers is 14 times their HCF
One number = 36
Sum of LCM and HCF = 270
Concept Used:
LCM × HCF = Product of two numbers
Calculation:
Let the HCF be x.
So, LCM = 14x
According to the question,
⇒ x + 14x = 270
⇒ x = (270/15) = 18
⇒ HCF = 18 and LCM = 14 × 18 = 252
Let the other number be z.
⇒ 18 × 252 = 36 × z
⇒ z = (18×252)/36 = 18 × 7 = 126
Therefore, the other number is 126.
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Most Upvoted Answer
The LCM of two numbers is 14 times their HCF. If one of the numbers is...
Given:
LCM of two numbers is 14 times their HCF
One number = 36
Sum of LCM and HCF = 270
Concept Used:
LCM × HCF = Product of two numbers
Calculation:
Let the HCF be x.
So, LCM = 14x
According to the question,
⇒ x + 14x = 270
⇒ x = (270/15) = 18
⇒ HCF = 18 and LCM = 14 × 18 = 252
Let the other number be z.
⇒ 18 × 252 = 36 × z
⇒ z = (18×252)/36 = 18 × 7 = 126
Therefore, the other number is 126.
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Community Answer
The LCM of two numbers is 14 times their HCF. If one of the numbers is...
To find the other number, we need to find the HCF and LCM of the two numbers given in the problem.

Let's assume the other number as 'x'.
Given:
One number = 36
Sum of LCM and HCF = 270

Finding the HCF:
We know that HCF (Highest Common Factor) is the largest number that divides both the given numbers.
HCF of 36 and 'x' = 270 - LCM

Finding the LCM:
We know that LCM (Least Common Multiple) is the smallest number that is divisible by both the given numbers.
LCM of 36 and 'x' = 14 times their HCF

Equation 1: HCF of 36 and 'x' = 270 - LCM
Equation 2: LCM of 36 and 'x' = 14 * HCF

Now, let's solve these equations to find the value of 'x'.

HCF of 36 and 'x' = 270 - LCM
LCM of 36 and 'x' = 14 * HCF

Substituting the value of LCM from Equation 2 into Equation 1, we get:
HCF of 36 and 'x' = 270 - (14 * HCF)

Simplifying the equation, we get:
HCF of 36 and 'x' + 14 * HCF = 270

Combining like terms, we get:
15 * HCF = 270

Dividing both sides of the equation by 15, we get:
HCF = 18

Now, substituting the value of HCF into Equation 2, we get:
LCM of 36 and 'x' = 14 * 18
LCM of 36 and 'x' = 252

We know that LCM of two numbers is the product of the numbers divided by their HCF.
Therefore, (36 * 'x') / 18 = 252

Simplifying the equation, we get:
'x' = 252 * 18 / 36
'x' = 126

Hence, the other number is 126 (option A).
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The LCM of two numbers is 14 times their HCF. If one of the numbers is 36 and the sum of the LCM and the HCF is 270, then the other number is:a)126b)144c)252d)234Correct answer is option 'A'. Can you explain this answer?
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The LCM of two numbers is 14 times their HCF. If one of the numbers is 36 and the sum of the LCM and the HCF is 270, then the other number is:a)126b)144c)252d)234Correct answer is option 'A'. Can you explain this answer? for Airforce X Y / Indian Navy SSR 2025 is part of Airforce X Y / Indian Navy SSR preparation. The Question and answers have been prepared according to the Airforce X Y / Indian Navy SSR exam syllabus. Information about The LCM of two numbers is 14 times their HCF. If one of the numbers is 36 and the sum of the LCM and the HCF is 270, then the other number is:a)126b)144c)252d)234Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Airforce X Y / Indian Navy SSR 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The LCM of two numbers is 14 times their HCF. If one of the numbers is 36 and the sum of the LCM and the HCF is 270, then the other number is:a)126b)144c)252d)234Correct answer is option 'A'. Can you explain this answer?.
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