Find the GCD and the LCM:

(1) 250, 150

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Solution

Prime factorisation of 250:
$\begin{matrix} 2 & 250 \\ 5 & 125 \\ 5 & 25 \\ 5 & 5 \\ 1 \end{matrix}$
⇒ 250 = 2 × 5 × 5 × 5

Prime factorisation of 150:
$\begin{matrix} 2 & 150 \\ 3 & 75 \\ 5 & 25 \\ 5 & 5 \\ 1 \end{matrix}$
⇒ 250 = 2 × 3 × 5 × 5
GCD = 2 × 5 × 5 = 50

$\begin{matrix} 2 & 250, 150 \\ 3 & 125, 75 \\ 5 & 125, 25 \\ 5 & 25, 5 \\ 5 & 5, 1 \\ 1, 1 \end{matrix}$
LCM = 2 × 3 × 5 × 5 × 5 = 750

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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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g c d (b_{3}, c_{3}) = a_{2}

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