Question

If $ D_{30} $ is the set of all divisors of $ 30, x, y \in D_{30} $ , we define $ x + y = LCM(x, y), x \cdot y = GCD (x, y) $ , $ x' = \frac{30}{x} $ and $ f(x, y, z) = (x + y) \cdot (y' + z) $ , then $ f(2, 5, 15) $ is equal to

• A. $ 2 $
• B. $ 5 $
• C. $ 10 $
• D. $ 15 $

Answer 1

Answer: (C)

$ D_{30}=\{1,2,3, 5,6,10,15,30\} $
$f(2,5,15) =(2+5) \cdot\left(5'+15\right) $
$= 10 \cdot\left(\frac{30}{5}+15\right) $
$= 10(6+15) $
$= 10 \cdot 30$
$= 10$