Multiple choice

There are two numbers which are greater than 21, and their LCM and HCF are 3003 and 21, respectively. What is the sum of these numbers?

  1. 504

  2. 508

  3. 514

  4. 528
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A Correct answer
Explanation

Let the numbers be 21a and 21b where a and b are coprime. 21 * a * b = 3003, so a * b = 143. Factors of 143 are (1, 143) and (11, 13). Since numbers > 21, we use (11, 13). Numbers are 21*11=231 and 21*13=273. Sum = 504.

AI explanation

Using the identity that the product of two numbers equals their LCM multiplied by their HCF, we get 3003 times 21, which is 63063. Assuming the numbers are 21a and 21b where a and b are coprime, their product gives 441ab, leading to ab = 143. The valid factor pairs of 143 are (1, 143) and (11, 13), but since both numbers are greater than 21, the co-prime factors must be 11 and 13. The required sum of the two numbers is (21 multiplied by 11) plus (21 multiplied by 13), which equals 231 plus 273, resulting in a total of 504.

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