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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?

\[\huge \color{red}{2}, \color{green}{-4}\]

Find the lowest common multiple of the two numbers above.

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

There will be separate rows for boys and girls.

Each row will have an equal number of students.

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

\[ \large n! + 1 \qquad \qquad (n+1)! + 1 \]

If \(n\) is a positive integer, find the greatest common divisor of the two numbers above.

\[\]**Notation**: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

Positive integers from 1 to 3141 (inclusive) are written on a blackboard. Two numbers from the board are chosen, erased, and their greatest common divisor is written.

This is repeated until only one number remains on the blackboard. What is the maximum possible value of this number?

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