Multiple choice

Two numbers both greater than $29$, have $HCF = 29$ and $LCM = 4147$. The sum of the numbers is

  1. $666$
  2. $669$
  3. $696$
  4. $966$
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C Correct answer
Explanation

Let the numbers be 29a and 29b where a and b are coprime. 29 * a * b = 4147, so ab = 143. Factors of 143 are (1, 143) and (11, 13). Since both numbers > 29, we use 11 and 13. The numbers are 29*11 = 319 and 29*13 = 377. Sum = 319 + 377 = 696.

AI explanation

Let the numbers be 29a and 29b, where a and b are coprime. The LCM is 29ab = 4147, so ab = 143. The coprime factor pairs of 143 are (1, 143) and (11, 13), but both numbers must be greater than 29. This gives the pair (11, 13), resulting in the numbers 319 and 377. Their sum is 319 + 377 = 696. The sum is 696.

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