Multiple choice

The LCM of two numbers is 588 and their product is 57624. Find their difference.

  1. 98

  2. 196

  3. 294

  4. 480

  5. 520
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A Correct answer
AI explanation

Using the identity Product = HCF times LCM, we find the HCF by dividing 57624 by 588. This gives an HCF of 98. Let the two numbers be 98x and 98y, where x and y are coprime, so their LCM is 98xy = 588, yielding xy = 6. The possible coprime pairs for 6 are (1, 6) and (2, 3). Taking the pair (1, 6), the numbers are 98 and 588, making their difference 490. Taking the pair (2, 3), the numbers are 196 and 294, making their difference 98. The correct difference is 98.

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