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Find the greatest common factor
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Find the least common multiple
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$12$
Find the greatest common factor
$\color{#FF6800}{ 24 } , \color{#FF6800}{ 60 }$
$ $ Do prime factorization $ $
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 60 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = 2 ^ { 3 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 60 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \end{cases}$
$ $ Multiply all common prime factors, $ 2 , 3 $ , and choose the exponent of the power from one of equal to or less $ $
$\begin{cases} 24 = 2 ^ { 3 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 60 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \\ \text{Common factor} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = 2 ^ { 3 } \times 3 ^ { 1 } \\ 60 = 2 ^ { 2 } \times 3 ^ { 1 } \times 5 ^ { 1 } \\ \text{Common factor} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$ $ Common factor is the greatest common factor $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
$ $ Multiply $ 4 $ and $ 3$
$\color{#FF6800}{ 12 }$
$120$
Find the least common multiple
$\color{#FF6800}{ 24 } , \color{#FF6800}{ 60 }$
$ $ Do prime factorization $ $
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 60 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 60 = 2 ^ { 2 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \end{cases}$
$ $ Multiply all common prime factors, $ 2 , 3 $ , and choose the exponent of the power from one of equal to or greater $ $
$\begin{cases} 24 = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ 60 = 2 ^ { 2 } \times \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \times 5 ^ { 1 } \\ \text{Common factor} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} 24 = 2 ^ { 3 } \times 3 ^ { 1 } \\ 60 = 2 ^ { 2 } \times 3 ^ { 1 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \\ \text{Common factor} :\text{ } 2 ^ { 3 } \times 3 ^ { 1 } \end{cases}$
$ $ Multiply all non-common prime factors, $ 5 $ and choose the exponent of the power from one of equal to or greater $ $
$\begin{cases} 24 = 2 ^ { 3 } \times 3 ^ { 1 } \\ 60 = 2 ^ { 2 } \times 3 ^ { 1 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \\ \text{Least common multiple (LCM)} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$\begin{cases} \color{#FF6800}{ 24 } = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \\ \color{#FF6800}{ 60 } = \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \\ \text{Least common multiple (LCM)} :\text{ } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 1 } } \end{cases}$
$ $ 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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