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2015 AMC 12B Question 23

AMC12 · 2015 AMC 12B

Question 23

A rectangular box measures $a \times b \times c,$ where $a,$ $b,$ and $c$ are integers and $1 \le a \le b \le c.$ The volume and the surface area of the box are numerically equal. How many ordered triples $(a, b, c)$ are possible?
  1. $4$
  2. $10$
  3. $12$
  4. $21$
  5. $26$