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Greatest Common Divisor / Lowest Common Multiple

What is the largest number that can divide two numbers without a remainder? What is the smallest number that is divisible by two numbers without a remainder?

Greatest Common Divisor / Lowest Common Multiple: Level 2 Challenges

         

A number \(N\) when divided by 9 leaves the remainder of 5.

Find the remainder when the same number \(N\) is divided by 3.

There are 48 boys and 64 girls in your class. Your teacher plans to arrange your class into rows according to the following rules.

  1. There will be separate rows for boys and girls.

  2. Each row will have an equal number of students.

What is the minimum number of rows possible to arrange your class?

\[\dfrac{n+1}{1},\ \dfrac{n+2}{2},\ \dfrac{n+3}{3},\ \dfrac{n+4}{4},\ \dfrac{n+5}{5}\]

With \(n=0\), all of the above numbers are integers (they all equal 1). What is the next positive integer \(n\) such that all of the above numbers are integers?

A teacher has 30 pens and 45 pencils that he wants to give to his students. If each student were to receive the same number of pens and the same numbers of pencils with none left over, then what is the maximum number of students that this teacher could have?

Image credit: Wikipedia Pens Pencils

Six bells, commencing tolling together, toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

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