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Formula
Find the greatest common factor
Find the least common multiple
$24,30$
$6$
Find the greatest common factor
$\color{#FF6800}{ 24 } , \color{#FF6800}{ 30 }$
 Do prime factorization 
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 30 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = 2 ^ { 3 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 30 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \end{cases}$
 Multiply all common prime factors, $2 , 3$ , and choose the exponent of the power from one of equal to or less 
$\begin{cases} 24 = 2 ^ { 3 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 30 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \\ \text{Common factor} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = 2 ^ { 3 } \times 3 ^ { 1 } \\ 30 = 2 ^ { 1 } \times 3 ^ { 1 } \times 5 ^ { 1 } \\ \text{Common factor} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
 Common factor is the greatest common factor 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } }$
 Simplify the expression 
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
 Multiply $2$ and $3$
$\color{#FF6800}{ 6 }$
$120$
Find the least common multiple
$\color{#FF6800}{ 24 } , \color{#FF6800}{ 30 }$
 Do prime factorization 
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 30 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 30 = 2 ^ { 1 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \end{cases}$
 Multiply all common prime factors, $2 , 3$ , and choose the exponent of the power from one of equal to or greater 
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 30 = 2 ^ { 1 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \\ \text{Common factor} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = 2 ^ { 3 } \times 3 ^ { 1 } \\ 30 = 2 ^ { 1 } \times 3 ^ { 1 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \\ \text{Common factor} :\text{ } 2 ^ { 3 } \times 3 ^ { 1 } \end{cases}$
 Multiply all non-common prime factors, $5$ and choose the exponent of the power from one of equal to or greater 
$\begin{cases} 24 = 2 ^ { 3 } \times 3 ^ { 1 } \\ 30 = 2 ^ { 1 } \times 3 ^ { 1 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \\ \text{Least common multiple (LCM)} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 24 } = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ \color{#FF6800}{ 30 } = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \\ \text{Least common multiple (LCM)} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
 Find the least common multiple 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } }$
 Simplify the expression 
$\color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 }$
 Multiply the numbers 
$\color{#FF6800}{ 120 }$
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