Question

Let S be the set of all ordered pairs $(x,y)$ of positive integers, with HCF(x, y)$=16$ and LCM(x, y)$=48000$. The number of elements in S is?

• A. $4$
• B. $8$
• C. $16$
• D. $32$

Answer 1

The correct option is B $8$

let numbers are $x=16\times a$ and $y=16\times b$, where $a$ and $b$ are co-prime numbers.

and $L.C.M(x,y)=16\times a\times b=16ab=48000\Rightarrow ab=3000$

factors of $3000=2\times 2\times 2\times 3\times 5\times 5\times 5$

possible values of $ab=1\times 3000,3\times 1000,8\times 375,$ and $24\times 125$

Thus, number of elements in $S=8$.