Bunuel 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
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of A and B)(least common multiple of A and B) = ABExample: A = 10 and B = 15
Greatest common divisor of 10 and 15 =
5Least common multiple of 10 and 15 =
30Notice that these values satisfy the above rule, since (
5)(
30) =
(10)(15)--------BACK TO THE QUESTION! ----------------------
One of the two integers is ZLet the other integer be Q.
So,
our goal is to determine the value of QGIVEN:
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) = ABAnd 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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