9. Several rectangular prisms with edge lengths of are combined in the same direction to form a cube with an edge length of 90. The number of small rectangular prisms that a diagonal of the cube passes through is:
Pick one
Solution
9. B.
Since the least common multiple of is 30, and the number of small rectangular prisms with edge lengths of that a diagonal of a cube with edge length 30 passes through is , therefore, the number of small rectangular prisms that a diagonal of a cube with edge length 90 passes through should be .
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.