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If LCM of two numbers is thrice the larger number and difference between the smaller number and the HCF is 14. Then, find out the smaller number of the two numbers.
  • a)
    16
  • b)
    23
  • c)
    21
  • d)
    42
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If LCM of two numbers is thrice the larger number and difference betwe...
Solution: Let the larger number be x and the smaller number be y.
It is given that LCM is thrice of the larger number,
Therefore, LCM = 3x      ----(i)
It is also given that difference between the smaller number and the HCF is 14,
Therefore, y – HCF = 14
HCM = y – 14      ----(ii)
We know that product of two numbers = LCM × HCF
Therefore, x × y = 3x × (y – 14)      (from (i) and (ii))
y = 3(y – 14)
y = 3y – 42
2y = 42
y = 21
Hence, the smaller number is 21.
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Most Upvoted Answer
If LCM of two numbers is thrice the larger number and difference betwe...
Given Information:
- LCM of two numbers is thrice the larger number
- Difference between the smaller number and the HCF is 14

Solution:

Let's assume the two numbers are A and B, where A is the larger number and B is the smaller number.

Given:
- LCM(A,B) = 3A
- B - HCF(A,B) = 14

Expressing LCM in terms of HCF:
- LCM(A,B) = (A * B) / HCF(A,B)

Substitute the given values:
- 3A = (A * B) / HCF(A,B)
- 3A = AB / HCF(A,B)

Since A is the larger number, let's consider A = k * HCF(A,B) where k is a positive integer:
- 3(k * HCF(A,B)) = k * HCF(A,B) * B / HCF(A,B)
- 3k = B

Now, substitute B = 3k into the second equation:
- 3k - HCF(3k, k) = 14
- 3k - k = 14
- 2k = 14
- k = 7

Therefore, the smaller number B = 3k = 3 * 7 = 21.
So, the smaller number of the two numbers is 21, which corresponds to option 'C'.
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If LCM of two numbers is thrice the larger number and difference between the smaller number and the HCF is 14. Then, find out the smaller number of the two numbers.a)16b)23c)21d)42Correct answer is option 'C'. Can you explain this answer?
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