Madina and Katy are in different physics classes. Madina's physics tests always have exactly 45 questions on them, while Katy's physics tests always have exactly 30 on them. By the end of the year, Madina and Katy have had the same total number of questions on all their physics tests. What is the minimum number of questions they each could have gotten during the year?

Each test of Madina and Katy will have 45 and 30 questions, respectively. The total number of questions they each could have gotten must be a multiple of both 45 and 30 because each class's total # of questions will be a multiple of the # of questions on 1 test, and the total number of questions will be the same.

We must find the least common multiple of the two numbers to find the minimum number of questions they each could have gotten.

We'll list out the first 3 multiples of each number.

{45, 90, 135...}

{30, 60, 90}

Within three multiples, we have found that the least common multiple is 90.

Now we know that Madina and Katy each had at least 90 questions this year.