Jane sells boxes of cookies for $8 each. sam sells boxes of cookies for $10 each. each of them sold the same dollar amount. it was the smallest dollar amount for which this was possible.

In order to solve this problem, we need to find the least common multiple of 8 and 10.  The first step to doing this is finding the prime factorization of 8 and 10.

8 is 2*2*2, and 10 is 2*5.  The two factors of 8 and 10 are 2 and 5.  Now, we multiply 2 by the greatest amount of times it occurs.  This is 3, coming from the prime factorization of 8.  Next, we multiply 5 by the greatest amount of times it occurs. This is simply 1, because it only pops up once.

This is: 2*2*2*5 = 40, so 40 is the least common multiple.  Because the least common multiple of 8 and 10, $40 is the smallest dollar amount that Jane and Sam could have made.