Skip-Count Multiples

Definition

Skip-Count Multiples in plain English

Pull Skip-Count Multiples when counting multiples in a range. Clues include how many multiples of 7 between 1 and 200. Blueprint: lfloor mathrmlast/k rfloor - lfloor (mathrmfirst-1)/k rfloor; use inclusion-exclusion for LCM unions when two bases are allowed. Listing multiples wastes time and misses endpoints, especially on inclusive vs exclusive borders. Write the floors carefully so the first and last multiples are not double-dropped. Micro-example: multiples of 7 from 1 to 50 inclusive: lfloor 50/7 rfloor - lfloor 0/7 rfloor = 7. For multiples of 6 or 15, add both counts then subtract multiples of mathrmLCM(6,15) = 30. Watch inclusive endpoints: if the range starts at 0 or at a multiple of k, the floor formula still handles it when you use first-1 carefully.

Practice Skip-Count Multiples

Which of the following inequalities correctly represents this range?

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