# Greatest Common Divisor (factor) - Least Common Multiple

## Greatest Common Factor GCF

Greatest common factor of two integers m and n is:

$GCF\left(m;n\right)=\left(m;n\right)=l$

Eeuclidean algorithm for computing the greates common factor GCF

Example: GCF (246;132)=(246;132)=6

$\begin{array}{ccc}{246}& =& {132}·1+{114}\\ {132}& =& {114}·1+{18}\\ {114}& =& {18}·6+{6}\\ {6}& =& \overline{)6}·1+0\end{array}\begin{array}{}\\ \\ \\ \end{array}$

## Least Common Multiple LCM

Least common multiple of two integers m and n is:

{formula_2329}

## Connection between the greatest common divisor (GCD) and the least common multiple (LCM)

$\left(m;n\right)·\left[m;n\right]=m·n$

Example: LCM (246;132)=[246;132]=5412

$\left[246;132\right]=\frac{246·132}{\left(246;132\right)}=\frac{246·132}{6}=5412$

## Relative Primes

Two integers m and n are relatively prime if they share no common positive factors (divisors) except 1. GCF(m;n)=[m;n]=1

Keywords: Greatest Common Divisor (factor) - Least Common Multiple