Multiple choice

The HCF of 2 numbers is 11 and their LCM is 693 If their sum is 176 find the numbers

  1. 99, 77

  2. 110, 66

  3. 88, 77

  4. 121, 44
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A Correct answer
Explanation

Given HCF = 11, the numbers are 11x and 11y where x and y are coprime. Their product is 11x * 11y = 11 * 693, so xy = 63. Their sum is 11(x + y) = 176, so x + y = 16. The pairs of factors of 63 that sum to 16 are 7 and 9. Thus, the numbers are 11*7 = 77 and 11*9 = 99.

AI explanation

Let the two numbers be 11x and 11y, where x and y are coprime. Their sum is 11x plus 11y = 176, which simplifies to x plus y = 16. Checking the given pairs, 99 and 77 have a sum of 176, an HCF of 11, and an LCM of 693. The numbers are 99 and 77.

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