# Progressive Intersections

**Number Theory**Level 4

\({AP}_{ 1 }=\quad 10,\quad 17,\quad 24,\quad 31,\quad \ldots\\

{ AP }_{ 2 }=\quad 9,\quad 14,\quad 19,\quad 24,\quad \ldots\\

{ AP }_{ 3 }= \quad 5,\quad 9,\quad 13,\quad 17,\quad\ldots\\

{ AP }_{ 4 }=\quad 5,\quad 8,\quad 11,\quad 14,\quad \ldots\)

Consider the four arithmetic progressions above. What is the smallest 4-digit number common to all these progressions?