If a and b are positive integers, a > b, the greatest common factor of

a = 3*5
b = 2*5
x=5

a-b = 5

GCF(a-b, b) = GCF(5, 10) = 10

option D --> (a-b)*b/x = 5*10/5 = 10

Let a =5×5
b =4×5
Therefore a-b =5
x = 5
y =4×5×5=100
LCM of (a-b,b)
LCM of (5, 20) =20
(a-b)b/x = 5×20/5=20
Option D is the answer

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Can not we take a = 20 & b = 10 ?

The problem with 20 and 10 is how will you differentiate between option A and D both of them are comming correct.

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We can let a = 5 and b = 2. So x = GCF(5, 2) = 1, and y = LCM(5, 2) = 10. Since a - b = 5 - 2 = 3, we have LCM(3, 2) = 6. We can check which answer choice will also give us the value of 6.

A. x = 1 → This is not 6.

B. y = 10 → This is not 6.

C. (a - b)b = (5 - 2)(2) = 6 → This is 6, but we need to make sure the last two choices aren’t 6, either.

D. (a - b)b/x = (5 - 2)(2)/1 = 6 → This is also 6.

E. x(a - b) = 1(5 - 2) = 3 → This is not 6.

We see that both C and D give us 6. To determine which one is the correct answer, we need to use a different pair of values of a and b with a GCF greater than 1. Letting a = 6 and b = 4, we see that x = GCF(6, 4) = 2 and y = LCM(6, 4) = 12. Since a - b = 6 - 4 = 2, we have LCM(2, 4) = 4. We can check which answer choice (between C and D) will also give us the value of 4.

C. (a - b)b = (6 - 4)(4) = 8 → This is not 4.

D. (a - b)b / x = (6 - 4)(4)/2 = 8/2 = 4 → This is 4.

Answer: D

Let a and b be equal to 15 and 10 respectively.
(a < b)

GCF(a, b)= GCF(15, 10) = x=5
LCM(a, b)= LCM(15, 10) = y=30
---> LCM (a-b, b)= LCM (15-10, 10) = 10

Only answer option D \(\frac{(a-b)b}{x} = \frac{(15-10)*10}{5}\) gives the same answer.

Answer (D)

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