Question

If LCM of 'a' and 18 is 36 and HCF of 'a' and 18 is 2 , then find the value of 'a'.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{HCF}\mathrm{of}2\mathrm{numbers}\times \mathrm{LCM}\mathrm{of}2\mathrm{numbers}=\mathrm{Product}\mathrm{of}2\mathrm{numbers}. \\ \mathrm{Here}\mathrm{the}\mathrm{numbers}\mathrm{are}\mathrm{a}\mathrm{and}18. \\ \mathrm{Now},\mathrm{HCF}\left(\mathrm{a},18\right)\times \mathrm{LCM}\left(\mathrm{a},18\right)=\mathrm{a}\times 18 \\ \Rightarrow 2\times 36=18\mathrm{a} \\ \Rightarrow \mathrm{a}=\frac{72}{18}=4 \end{gathered}$$