Question

The sum and difference of two numbers are 42 and 6 respectively. If the LCM of these two numbers is 72 , then the ratio of their HCF and LCM is?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numbers}\mathrm{are}x\mathrm{and}y. \\ \mathrm{According}\mathrm{to}\mathrm{question}. \\ x+y=42......\left(1\right) \\ x-y=6.....\left(2\right) \\ \mathrm{Adding}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get} \\ 2x=48 \\ \Rightarrow x=24 \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get}y=18 \\ \mathrm{So}\mathrm{the}\mathrm{two}\mathrm{numbers}\mathrm{are}24\mathrm{and}18 \\ \mathrm{Now},\mathrm{LCM}=72 \\ \mathrm{HCF}\times \mathrm{LCM}=\mathrm{product}\mathrm{of}2\mathrm{numbers} \\ \Rightarrow \mathrm{LCM}=\frac{\mathrm{product}\mathrm{of}2\mathrm{numbers}}{\mathrm{HCF}}=\frac{24\times 18}{72}=6 \\ \mathrm{now}, \\ \frac{\mathrm{LCM}}{\mathrm{HCF}}=\frac{6}{72}=\frac{1}{12} \end{gathered}$$