# 10. Find the LCM of the following numbers : (a) 9 and 4      (b) 12 and 5     (c) 6 and 5     (d) 15 and 4 Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

P Pankaj Sanodiya

(a) LCM = 2 $\times$ 2 $\times$ 3 $\times$ 3 = 36

$\begin{array}{|c|c|}\hline 2 & {9,4} \\ \hline 2 & {9,2} \\ \hline 3 & {9,1} \\ \hline 3 & {3,1} \\ \hline & {1,1} \\ \hline\end{array}$

(b) LCM = 2 $\times$ 2 $\times$ 3 $\times$ 5 = 60

$\begin{array}{|c|c|}\hline 2 & {12,5} \\ \hline 2 & {6,5} \\ \hline 3 & {3,5} \\ \hline 5 & {1,5} \\ \hline & {1,1} \\ \hline\end{array}$

(c) LCM = 2 $\times$ 3 $\times$ 5 = 30

$\begin{array}{|c|c|}\hline 2 & {6,5} \\ \hline 3 & {3,5} \\ \hline 5 & {1,5} \\ \hline & {1,1} \\ \hline\end{array}$

(d) LCM = 2 $\times$ 3 $\times$ 5 = 30

$\begin{array}{|c|c|}\hline 2 & {15,4} \\ \hline 2 & {15,2} \\ \hline 3 & {15,1} \\ \hline 5 & {5,1} \\ \hline & {1} \\ \hline\end{array}$

Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers.

When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3.

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