Multiple choice

Take the smallest odd composite number and largest three digit prime number. What is the difference between the LCM and the HCF of these two numbers?

  1. $8336$
  2. $8972$
  3. $8874$
  4. $8566$
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B Correct answer
Explanation

Smallest odd composite number is 9. Largest three-digit prime is 997. HCF(9, 997) = 1 (since 997 is prime and not divisible by 3). LCM(9, 997) = 9 * 997 = 8973. Difference = 8973 - 1 = 8972.

AI explanation

The smallest odd composite number is 9 and the largest three-digit prime number is 997. Since 9 and 997 share no common factors, their highest common factor is 1 and their least common multiple is their product, 9 times 997, which equals 8973. The difference between the LCM and HCF is 8973 minus 1, resulting in 8972. Therefore, the required difference is 8972.

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