Question

the greatest common divisor of two integers is $(x 2)$ and their least common multiple is $x(x 2)$, where $x$ is a positive integer. if one of the integers is 24, what is the smallest possible value of the other one?

Answer 1

The greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

As per the question statement, the greatest common divisor of two integers is (x+2) and the least common multiple x(x+2). It is given that one of the integers is 24.

Let us assume that "b" is the value of other one.

greatest common divisor(24,b) = (x+2)

least common multiple(24,b) = x(x+2)

Formula:

greatest common divisor(24,b)*least common multiple(24,b) = 24*b

24*b = (x+2)*x(x+2)

$b = \frac{x(x+2)^{2} }{24}$

Hence, the smallest possible value of the other one is "6" and x = 4.

Hence, the greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

• Common divisor: A number or expression that evenly divides two or more other numbers or phrases.
• Common multiple: A number into which every number in a particular collection may be split equally.

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