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Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
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$ \begin{array}{|l} \llap{2~~~~} 12 \\ \hline \llap{2~~~~} 6 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array} $
$ \begin{array}{|l} \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array} $
$ \begin{array}{|l} \llap{3~~~~} 21 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array} $
$12 = 2 \times 2 \times 3$
$15 = 3 \times 5$
$21 = 3 \times 7$
Hence HCF $= 3$
LCM $ = 2 \times 2 \times 3 \times 5 \times 7 = 420$
$ \begin{array}{|l} \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array} $
$ \begin{array}{|l} \llap{3~~~~} 21 \\ \hline \llap{7~~~~} 7 \\ \hline 1 \end{array} $
$12 = 2 \times 2 \times 3$
$15 = 3 \times 5$
$21 = 3 \times 7$
Hence HCF $= 3$
LCM $ = 2 \times 2 \times 3 \times 5 \times 7 = 420$