Subject: General Aptitude · Chapter: H.C.F. and L.C.M. of Numbers · Exam: · Marks: · Difficulty:
The sum of two numbers is 2000 and their L.C.M. is 21879. The two numbers are
(a)1993, 7
(b)1991, 9
(c)1989, 11
(d)1987, 13
Answer
Answer (as printed): C
Explanation
Let the numbers be $x$ and $(2000-x)$. Then, their L.C.M. $=x(2000-x)$. So, $x(2000-x)=21879$ $\Leftrightarrow \quad x^{2}-2000 x+21879=0$ $\Leftrightarrow \quad(x-1989)(x-11)=0$ $\Leftrightarrow \quad x=1989$ or $x=11$. Hence, the numbers are 1989 and 11.
Explanation as extracted from the printed page; notation may be imperfect.