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The greatest common factor of two positive integers is X. The least co
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05 Jul 2021, 06:47
05 Jul 2021, 06:47
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The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + ⁄Y
A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + ⁄Y
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The greatest common factor of two positive integers is X. The least co
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05 Jul 2021, 07:20
05 Jul 2021, 07:20
1
Carcass wrote:
The greatest common factor of two positive integers is X. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y
A. XY⁄Z
B. XZ + YZ
C. X⁄Z + Y
D. X + Y⁄Z
E. X + Z⁄Y
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of A and B)(least common multiple of A and B) = AB
Example: A = 10 and B = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------
One of the two integers is Z
Let the other integer be Q.
So, our goal is to determine the value of Q
GIVEN:
The greatest common factor (divisor) of Z and Q is X.
The least common multiple of Z and Q is Y.
Take the formula: (greatest common divisor of A and B)(least common multiple of A and B) = AB
And plug in the given info to get: (X)(Y) = ZQ
In other words: XY = ZQ
Divide both sides by Z to get: XY/Z = Q
Answer: A
Cheers,
Brent
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
The greatest common factor of two positive integers is X. The least co
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28 Oct 2022, 08:22
28 Oct 2022, 08:22
1
Given that GCD of two positive integers = 3 and LCM of two positive integers = Y and one number is Z and we need to find the value of other integer
Theory: LCM of two Numbers * GCD of two numbers = Product of the numbers
=> LCM * GCD = Z * T (Assume T is the other integer)
=> Y * X = Z * T
=> T = \(\frac{XY}{Z}\)
So, Answer will be A
Hope it helps!
To learn more about LCM and GCD watch the following videos
Theory: LCM of two Numbers * GCD of two numbers = Product of the numbers
=> LCM * GCD = Z * T (Assume T is the other integer)
=> Y * X = Z * T
=> T = \(\frac{XY}{Z}\)
So, Answer will be A
Hope it helps!
To learn more about LCM and GCD watch the following videos
