Find the GCD and the LCM:

(6) 46, 51, 35

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Solution

Prime factorisation of 46:
$\begin{matrix} 2 & 46 \\ 23 & 23 \\ 1 \end{matrix}$
⇒ 46 = 2 × 23

Prime factorisation of 51:
$\begin{matrix} 3 & 51 \\ 17 & 17 \\ 1 \end{matrix}$
⇒ 51 = 3 × 17

Prime factorisation of 35:
$\begin{matrix} 5 & 35 \\ 7 & 7 \\ 1 \end{matrix}$
⇒ 35 = 5 × 7

GCD = 1

$\begin{matrix} 2 & 46, 51, 35 \\ 3 & 23, 51, 35 \\ 5 & 23, 17, 35 \\ 7 & 23, 17, 7 \\ 17 & 23, 17, 1 \\ 23 & 23, 1, 1 \\ 1, 1, 1 \end{matrix}$

LCM = 2 × 3 × 5 × 7 × 17 × 23 = 82110

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

a_{2} = g c d (b_{1}, c_{1}), b_{2} = g c d (c_{1}, a_{1}), c_{2} = g c d (a_{1}, b_{1}),

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