Find the GCD and the LCM:

(3) 32, 37

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Solution

Prime factorisation of 32:
$\begin{matrix} 2 & 32 \\ 2 & 16 \\ 2 & 8 \\ 2 & 4 \\ 2 & 2 \\ 1 \end{matrix}$
⇒ 32 = 2 × 2 × 2 × 2 × 2

Prime factorisation of 37:
$\begin{matrix} 37 & 37 \\ 1 \end{matrix}$
⇒ 37 = 1 × 37
GCD = 1

$\begin{matrix} 2 & 32, 37 \\ 2 & 16, 37 \\ 2 & 8, 37 \\ 2 & 4, 37 \\ 2 & 2, 37 \\ 37 & 1, 37 \\ 1, 1 \end{matrix}$
LCM = 2 × 2 × 2 × 2 × 2 × 37 = 1184

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