A board game for 2 to 6 players has a deck of cards that can always 
be divided evenly among all the players. What is the smallest numbers 
of cards that are possible?

It's the LCM of 2,3,4,5,and 6

Start by listing them in a row with a vertical line on the left

          |   2  3  4  5  6
          |
          |

Think of a prime number that will divide evenly into 2 or more of these.
Pick prime number 2, write it to the left of the vertical line:

       2  |   2  3  4  5  6
          |
          |

Divide 2 into each number that 2 will divide evenly into and put what
you get underneath.  Bring the other numbers down:

       2  |   2  3  4  5  6
          |   1  3  2  5  3
          |


Think of a prime number that will divide evenly into 2 or more of these
on the bottom line. Pick prime number 3, write it to the left of the 
vertical line:

       2  |   2  3  4  5  6
       3  |   1  3  2  5  3
          |

Divide 3 into each number that 3 will divide evenly into and put what
you get underneath.  Bring the other numbers down:

       2  |   2  3  4  5  6
       3  |   1  3  2  5  3
          |   1  1  2  5  1

There is no prime that will divide evenly into two of the numbers
on the bottom line. So we multiply down the left side and across the
bottom

2×3×1×1×2×5×1 = 60

We would need 60 cards

Edwin
AnlytcPhil@aol.com