Question

Last year, Riley's history and math classes had regular tests. Each history test had 11 questions and each math test had 6 questions. If Riley had to answer the same number of history questions and math questions last year, what is the smallest number of each type of question she must have answered?

Answer 1

The smallest number of history and math questions Riley must have answered is determined by the least common multiple (LCM) of 11 and 6, which is 66.

Step-by-step explanation:

The student has asked about finding the smallest number of history and math questions Riley must have answered if each history test had 11 questions and each math test had 6 questions, and she had to answer the same number of questions for both subjects last year.

This is a problem of finding the least common multiple (LCM) of two numbers, which is, in this case, the smallest common multiple of 11 (history questions per test) and 6 (math questions per test).

To find the LCM of 11 and 6, we can list the multiples of each number until we find a common multiple:

• Multiples of 11: 11, 22, 33, 44, 55, 66,...
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66,...

From these lists, we can see that 66 is the first multiple they have in common. Therefore, the smallest number of questions Riley must have answered for both history and math is 66.