Multiple choice

The LCM and HCF of two numbers are 1001 and 7 respectively. How many such pairs are possible?

  1. 0

  2. 1

  3. 2

  4. None of these
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C Correct answer
Explanation

LCM = 1001, HCF = 7. Numbers are 7a and 7b where a, b are coprime. 7 * a * b = 1001, so a * b = 143. Pairs (a, b) such that gcd(a, b) = 1 are (1, 143) and (11, 13). Thus, 2 pairs are possible.

AI explanation

Let the two numbers be 7x and 7y, where x and y are coprime natural numbers. Since the product of the numbers equals the product of their LCM and HCF, we have 7x times 7y = 1001 times 7, which simplifies to xy = 143. The coprime pairs of factors for 143 are (1, 143) and (11, 13), meaning 2 such pairs are possible.

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