Question
Find the $LCM$ and $HCF$ of the following integer by applying the prime factorisation method.
$12, 15$ and $21$
$12, 15$ and $21$
✓
Answer
$12 = 2 \times 2 \times 3$
$15 = 5 \times 3$
$21 = 7 \times 3$
$3$ is common for all, it means $HCF$ of $12, 15$ & $21$ is $3$
Now calculate $LCM$ of $12, 15, 21$
$\begin{array}{c|c} 2 & 12-15-21 \\ \hline 2 & 6-15-21\\\hline3 & 3-15-21\\\hline 5 & 1-5-7\\\hline7 & 1-1-7\\\hline & 1-1-1\end{array}$
So $LCM$ of $12, 15, 21 is 2 \times 2 \times 3 \times 5 \times 7$
$= 420$
From the above, $HCF (12, 15, 21) = 3$ and $LCM (12, 15, 21) = 420$
$15 = 5 \times 3$
$21 = 7 \times 3$
$3$ is common for all, it means $HCF$ of $12, 15$ & $21$ is $3$
Now calculate $LCM$ of $12, 15, 21$
$\begin{array}{c|c} 2 & 12-15-21 \\ \hline 2 & 6-15-21\\\hline3 & 3-15-21\\\hline 5 & 1-5-7\\\hline7 & 1-1-7\\\hline & 1-1-1\end{array}$
So $LCM$ of $12, 15, 21 is 2 \times 2 \times 3 \times 5 \times 7$
$= 420$
From the above, $HCF (12, 15, 21) = 3$ and $LCM (12, 15, 21) = 420$
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