Question

Lcm of 2/9 , 7/8 , 6/10

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}, \\ \mathrm{LCM}\mathrm{of}\mathrm{fractions}=\frac{\mathrm{LCM}\mathrm{of}\mathrm{numerators}}{\mathrm{HCF}\mathrm{of}\mathrm{denominators}} \\ \mathrm{So},\mathrm{LCM}\mathrm{of}\frac{2}{9},\frac{7}{8}\mathrm{and}\frac{6}{10}=\frac{\mathrm{LCM}\mathrm{of}2,7\mathrm{and}6}{\mathrm{HCF}\mathrm{of}9,8\mathrm{and}10} \\ \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}2,7\mathrm{and}6\mathrm{is}:- \\ 2=2 \\ 7=7 \\ 6=2\times 3 \\ \therefore \mathrm{LCM}\left(2,7,6\right)=2\times 7\times 3=42 \\ \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}9,8\mathrm{and}10 \\ 9=3\times 3 \\ 8=2\times 2\times \\ 10=2\times 5 \\ \therefore \mathrm{HCF}\left(9,8\mathrm{and}10\right)=1 \\ \mathrm{Therefore},\mathrm{LCM}\mathrm{of}\frac{2}{9},\frac{7}{8}\mathrm{and}\frac{6}{10}=\frac{42}{1}=42 \end{gathered}$$