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SMO 2017 Junior Round 1 Question 9

SMO · SMO 2017 Junior Round 1

Question 9

Let $a$ and $b$ be positive integers. If the highest common factor of $a$ and $b$ is 6 and the lowest common multiple of $a$ and $b$ is $2^3 3^4 5^6$, how many possible values are there for $a$?
  1. $2$
  2. $4$
  3. $8$
  4. $14$
  5. $16$