Question
Find the $LCM$ and $HCF$ of the following integer by applying the prime factorisation method.
$8, 9$ and $25$
$8, 9$ and $25$
✓
Answer
$8 = 2^3 \times 1$
$9 = 3^2 \times 1$
$25 = 5^2 \times 1$
LCM of $8, 9, 25$
$\begin{array}{c|c} 2 & 8-9-25 \\ \hline 2 & 4-9-25\\\hline2 & 2-9-25\\\hline 3 & 1-9-25\\\hline3 & 1-3-25\\\hline 5 & 1-1-25\\\hline5&1-1-5\\\hline & 1-1-1\end{array}$
So $LCM$ of $8, 9, 25$ is $= 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5$
$= 1800$
From the above $HCF (8, 9, 25) = 1$ and $LCM (8, 9, 25) = 1800.$
$9 = 3^2 \times 1$
$25 = 5^2 \times 1$
LCM of $8, 9, 25$
$\begin{array}{c|c} 2 & 8-9-25 \\ \hline 2 & 4-9-25\\\hline2 & 2-9-25\\\hline 3 & 1-9-25\\\hline3 & 1-3-25\\\hline 5 & 1-1-25\\\hline5&1-1-5\\\hline & 1-1-1\end{array}$
So $LCM$ of $8, 9, 25$ is $= 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5$
$= 1800$
From the above $HCF (8, 9, 25) = 1$ and $LCM (8, 9, 25) = 1800.$
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