Question

at the factory, a baseballcard is placed in every 9th package of cereal. a football card is placed in every 25th package of the cereal. what is the first package that gets both a baseball amd football card

Answer 1

I believe that is gonna be the 225 package.
Thats the lowest number that both 25 and 9 go into

Answer 2

Answer: Here we are looking for the least common multiple (LCM) between 9 and 25, this is the first number which the sets {9, 18 ,27...} and {25, 50, 75...} have in common, where the first set is the set of the packages with a baseball card, and the second is the one with the football card.

the LCM between two numbers is

LCM(9,25) = 9*25/(gcd(9,25))

where gcd is the greatest common divisor between 9 and 25, in this case is 1, because 9 is only divided by 3, and 25 is only divided by 5.

then LCM (9,25) = 9*25 = 225.

then in the 225 package, you will have a football card, and a baseball card.