11. Find the LCM of the following numbers in which one number is the factor of the other.
(a) 5, 20      (b) 6, 18      (c) 12, 48      (d) 9, 45
What do you observe in the results obtained?

Answers (1)

(a) LCM = 2 \times 2 \times 5 = 20

\begin{array}{|c|c|}\hline 2 & {5,20} \\ \hline 2 & {5,10} \\ \hline 5 & {5,5} \\ \hline & {1,1} \\ \hline\end{array}

(b) LCM = 2 \times\times 3 = 18

\begin{array}{|c|c|}\hline 2 & {6,18} \\ \hline 3 & {3,9} \\ \hline 3 & {1,3} \\ \hline & {1,1} \\ \hline\end{array}

(c) LCM = 2 \times 2 \times 2 \times 2 \times 3 = 48

\begin{array}{|c|c|}\hline 2 & {12,48} \\ \hline 2 & {6,24} \\ \hline 2 & {3,12} \\ \hline 2 & {3,12} \\ \hline 3 & {3,3} \\ \hline & {1,1} \\ \hline\end{array}

(d) LCM = 3 \times 3 \times 5 = 45

\begin{array}{|c|c|}\hline 3 & {9,45} \\ \hline 3 & {3,15} \\ \hline 5 & {1,5} \\ \hline & {1,1} \\ \hline\end{array}

Yes, it can be observed that in each case, the LCM of the given numbers is the larger number. When one number is a factor of the other number, their LCM will be the larger number.

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