Class 6 Playing with Numbers Exercise 2.9

\begin{array}{l} \text {Q1. Determine the L.C.M. of the numbers given below: } \\ (i) \quad 48,60 \\ (ii) \quad 42,63 \\ (iii) \quad 18,17 \\ (iv) \quad 15,30,90 \\ (v) \quad 56,65,85 \\ (vi) \quad 180,384,144 \\ (vii) \quad 108,135,162 \\ (viii) \quad 28,36,45,60 \\ \\\text {Sol. } \\(i) \quad 48,60 \\ \end{array}\begin{array}{l|l} 2 & 48,60 \\ \hline 2 & 24,30 \\ \hline 2 & 12,15 \\ \hline 2 & 6, 15 \\ \hline 3 & 3, 15 \\ \hline 5 & 1,5 \\ \hline & 1,1 \end{array} \begin{array}{l} \text {LCM of 48 and 60} =2 \times 2 \times 2 \times 2 \times 3 \times 5 \\ = 240 \\ \\(ii) \quad 42,63 \\ \end{array}\begin{array}{l|l} 2 & 42,63 \\ \hline 3 & 21,63 \\ \hline 7 & 7,21 \\ \hline 3 & 1, 3 \\ \hline & 1,1 \end{array} \begin{array}{l} \text {LCM of 42 and 63} =2 \times 3 \times 3 \times 7 \\ = 126 \\ \\(iii) \quad 18,17 \\ \end{array}\begin{array}{l|l} 2 & 18,17 \\ \hline 3 & 9,17 \\ \hline 3 & 3,17 \\ \hline 17 & 1, 17 \\ \hline & 1,1 \end{array} \begin{array}{l} \text {LCM of 18 and 17} =2 \times 3 \times 3 \times 17\\ =306 \\ \\(iv) \quad 15,30,90 \\ \end{array}\begin{array}{l|l} 5 & 15,30,90 \\ \hline 3 & 3,6,18 \\ \hline 2 & 1,2,6 \\ \hline 3 & 1,1,3 \\ \hline & 1,1,1 \end{array} \begin{array}{l} \text {LCM of 15,30 and 90} =2 \times 3 \times 3 \times 5\\ =90 \\ \\(v) \quad 56,65,85 \\ \end{array}\begin{array}{l|l} 2 & 56,65,85 \\ \hline 2 & 28,65,85 \\ \hline 2 & 14,65,85 \\ \hline 7 & 7,65,85 \\ \hline 13 & 1,65,85 \\ \hline 5 & 1,5,85 \\ \hline 17 & 1,1,17 \\ \hline & 1,1,1 \end{array}\begin{array}{l} \text {LCM of 56,65 and 85} =2 \times 2 \times 2 \times 5 \times 7 \times 13 \times 17 \\ =61880 \\ \\(vi) \quad 180,384,144 \\ \end{array}\begin{array}{l|l} 2 & 180,384,144 \\ \hline 2 & 90,192,72 \\ \hline 2 & 45,96,36 \\ \hline 2 & 45,48,18 \\ \hline 2 & 45,24,9 \\ \hline 2 & 45,12,9 \\ \hline 2 & 45,6,9 \\ \hline 3 & 45,3,9 \\ \hline 3 & 15,1,3 \\ \hline 5 & 5,1,1 \\ \hline & 1,1,1 \end{array} \begin{array}{l} \text {LCM of 180,384 and 144} =2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \\ =5760\\ \\(vii) \quad 108,135,162 \\ \end{array}\begin{array}{l|l} 2 & 108,135,162 \\ \hline 2 & 54,135,81 \\ \hline 3 & 27,135,81 \\ \hline 3 & 9,45,27 \\ \hline 3 & 3,15,9 \\ \hline 3 & 1,5,3 \\ \hline 5 & 1,5,1 \\ \hline & 1,1,1 \end{array} \begin{array}{l} \text {LCM of 108,135 and 162} =2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5 \\ =1620 \\ \\(viii) \quad 28,36,45,60 \\ \\\end{array}\begin{array}{l|l} 2 & 28,36,45,60 \\ \hline 2 & 14,18,45,30 \\ \hline 3 & 7,9,45,15 \\ \hline 3 & 7,3,15,5 \\ \hline 5 & 7,1,5,5 \\ \hline 7 & 7,1,1,1 \\ \hline & 1,1,1,1 \\\end{array}\begin{array}{l} \text {LCM of 28,36,45 and 60} =2 \times 2 \times 3 \times 3 \times 5 \times 7 \\ =1260 \\ \end{array}