Multiple choice

The HCF and LCM of two numbers are 21 and 4641, respectively, if one of the numbers lies between 200 and 300 then find the two numbers

  1. 273,363

  2. 273,359

  3. 273,361

  4. 273,357
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D Correct answer
Explanation

HCF = 21. Numbers are 21a and 21b where a, b are coprime. LCM = 21ab = 4641. ab = 4641/21 = 221. Factors of 221 are 13 * 17. So numbers are 21*13 = 273 and 21*17 = 357.

AI explanation

Using the relationship Product = HCF times LCM, the product of the two numbers is 21 times 4641, which equals 97581. Let the numbers be 21x and 21y, so 21x times 21y equals 97581, giving 441xy = 97581 and xy = 221. The factors of 221 are 13 and 17, so the two numbers are 21 times 13 and 21 times 17, which are 273 and 357. The numbers are 273 and 357.

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