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What is the minimum number of books you will acquire for the class library, sothat they can be distributed equally among students of Section A or SectionB?

Question

What is the minimum number of books you will acquire for the class library, sothat they can be distributed equally among students of Section A or SectionB?

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Solution

To answer this question, we need to know the number of students in Section A and Section B. The minimum number of books you need to acquire is the least common multiple (LCM) of the two numbers.

Here are the steps to find the LCM:

  1. List the prime factors of each number.
  2. Multiply each factor the greatest number of times it occurs in either number.
  3. If the same factor occurs more than once in both numbers, you multiply it the greatest number of times it occurs.

For example, if Section A has 15 students and Section B has 25 students:

  1. The prime factors of 15 are 3 and 5. The prime factors of 25 are 5 and 5.
  2. The greatest number of 3s that appear in either is 1. The greatest number of 5s is 2.
  3. So, you multiply 3 once and 5 twice (because it's the greatest number of times it occurs in either number).

So, the LCM of 15 and 25 is 355 = 75.

Therefore, you would need a minimum of 75 books to distribute equally among the students of either Section A or Section B.

This problem has been solved

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