Find the GCD and the LCM:

(2) 96, 192

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Solution

Prime factorisation of 96:
$\begin{matrix} 2 & 96 \\ 2 & 48 \\ 2 & 24 \\ 2 & 12 \\ 2 & 6 \\ 3 & 3 \\ 1 \end{matrix}$
⇒ 96 = 2 × 2 × 2 × 2 × 2 × 3

Prime factorisation of 192:
$\begin{matrix} 2 & 192 \\ 2 & 96 \\ 2 & 48 \\ 2 & 24 \\ 2 & 12 \\ 2 & 6 \\ 3 & 3 \\ 1 \end{matrix}$
⇒ 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
GCD = 2 × 2 × 2 × 2 × 2 × 3 = 96

$\begin{matrix} 2 & 96, 192 \\ 2 & 48, 96 \\ 2 & 24, 48 \\ 2 & 12, 24 \\ 2 & 6, 12 \\ 2 & 3, 6 \\ 3 & 3, 3 \\ 1, 1 \end{matrix}$
LCM = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192

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