Question

If a positive integer y divides evenly into positive integer x, the LCM is ____ and the GCF is ____.

A) x, y
B) y, x
C) xy, 1
D) 1, xy

Answer 1

If a positive integer y divides evenly into positive integer x, the LCM is x and the GCF is y, which corresponds to answer choice A) x, y.

Step-by-step explanation:

If a positive integer y divides evenly into positive integer x, it means that x is a multiple of y. The Least Common Multiple (LCM) of any two numbers is the smallest number that is a multiple of both numbers. Since y divides x evenly, x is already a multiple of y, so the LCM of x and y is x itself.

Likewise, the Greatest Common Factor (GCF), also known as the greatest common divisor, is the largest number that divides both x and y evenly. Since y is a factor of x and there is no larger factor that divides x, the GCF here is y itself. Thus, the correct answer would be A) x, y.