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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


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?

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

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

For integral choices of \(x\) and \(y\), \[\text{LCM}(x, y) \leq xy.\]

Is the above statement true or false?

Clarification: The \(\text{LCM}\) is the Lowest Common Multiple of two numbers.

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.


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