Question

The number of ordered pairs $(x,y)$ such that $LCM$ of $x$ and $y$ is $2520$ is

• A. 150
• B. 225
• C. 315
• D. 450

Answer 1

Answer: (C)

$2520=2^3\times 3^2\times 5\times 7$
Ways to distribute $2^3$ to $(x,y)$ are:
$\left(2^3,1\right),\left(2^3,2\right),\left(2^3,2^2\right),\left(2^3,2^3\right),\left(1,2^3\right),\left(2,2^3\right),\left(2^2,2^3\right)$
$\therefore$ Number of ways of distribution $=2\times 3+1=7$
Similarly, other factors can also be distributed to $x$ and $y$.
Thus, the total number of ways
$=(2\times 3+1)(2\times 2+1)(2\times 1+1)(2\times 1+1)$
$=315$