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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? See more

Level 2

         

Find smallest positive \(a\) for \(a={ b }^{ 2 }={ c }^{ 3 }={ d }^{ 5 }\) such that \(a,b,c,d\) are distinct integers.

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

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

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

Find the least positive multiple of 7 which leaves a remainder of 4 when divided by any of 6, 9, 15 and 18.

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

Find the least common multiple (L.C.M.) of the two numbers above.

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
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