Civil Services Examination · প্রশ্ন 28

There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

6
7
8
More than 8

উত্তর দেখান ও ব্যাখ্যা

উত্তর: (D) More than 8

ব্যাখ্যা

1001 = 7 × 11 × 13. Many triples of divisors have LCM 1001 and HCF 1 (e.g. {1, 7, 143}, {7, 11, 13}, {1, 1001, x}, {7, 11, 91}...), well over 8. (Answer as per the official UPSC answer key.)