Find the GCD and the LCM:

(5) 405, 225

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Solution

Prime factorisation of 405:
$\begin{matrix} 3 & 405 \\ 3 & 135 \\ 3 & 45 \\ 3 & 15 \\ 5 & 5 \\ 1 \end{matrix}$
⇒ 405 = 3 × 3 × 3 × 3 × 5

Prime factorisation of 225:
$\begin{matrix} 3 & 225 \\ 3 & 75 \\ 5 & 25 \\ 5 & 5 \\ 1 \end{matrix}$
⇒ 225 = 3 × 3 × 5 × 5
GCD = 3 × 3 × 5 = 45

$\begin{matrix} 3 & 405, 225 \\ 3 & 135, 75 \\ 3 & 45, 25 \\ 3 & 15, 25 \\ 5 & 5, 25 \\ 5 & 1, 5 \\ 1, 1 \end{matrix}$
LCM = 3 × 3 × 3 × 3 × 5 × 5 = 2025

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a_{1}, b_{1}, c_{1}

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