| Example |
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\(9\times1=9 \\9\times2=18 \\9\times3=27 \\\)
\(9\) is multiplied by \(1,2,3,..\) will produce \(9,18,27,..\).
Thus, \(9,18,27,..\) is the multiples of \(9\).
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| Solution Methods |
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| Listing the common multiples: |
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(i) Determine the LCM of \(2\) and \(3\).
Multiples of \(2: 2,4,6,8,..\)
Multiples of \(3: 3, 6, 9,..\)
Thus, the lowest common multiple of \(2 \) and \(3\) is \(6\).
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| Repeated division: |
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(ii) Determine the LCM of \(3,6\) and \(9\).
\(\begin{array}{c} 3\\2\\3 \\\phantom{-} \end{array} \begin{array}{|c} \quad3,\,6,\,9\quad\\ \hline \quad1,\,2,\,3\quad\\ \hline \quad1,\,1,\,3\quad\\ \hline \quad1,\,1,\,1\quad\\ \end{array} \begin{array}{c}\end{array}\\\\\)
LCM of \(3,6\) and \(9\) is
\( 3\times2\times3 = 18\).
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| Prime factorisation: |
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(iii) Determine the LCM of \(3,8\) and \(12\).
\(\begin{aligned} 3&=\quad\quad\quad\quad\quad\,3 \\8&=2\times2\times2 \\12&=\quad\,\,\,\,\,2\times2\times3 \end{aligned}\\\\\)
LCM of \(3,8\) and \(12\) is
\(2\times2\times2\times3=24\).
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