Question

the L.C.M. of two number is six -times their H.C.F. if the difference between L.C.M and H.C.F is 60 and one of the two number is 36; fine the other number.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{other}\mathrm{number}=\mathrm{x} \\ \mathrm{Now},\mathrm{LCM}=6\mathrm{HCF}....\left(1\right) \\ \mathrm{Now},\mathrm{LCM}-\mathrm{HCF}=60 \\ \mathrm{Now},6\mathrm{HCF}-\mathrm{HCF}=60\left[\mathrm{Using}\left(1\right)\right] \\ \Rightarrow 5\mathrm{HCF}=60 \\ \Rightarrow \mathrm{HCF}=12 \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get}\mathrm{LCM}=6\times 12=72 \\ \mathrm{Now},\mathrm{LCM}\mathrm{of}2\mathrm{numbers}\times \mathrm{HCF}\mathrm{of}2\mathrm{numbers}=\mathrm{product}\mathrm{of}\mathrm{two}\mathrm{numbers} \\ \Rightarrow 72\times 12=36\times \mathrm{x} \\ \Rightarrow \mathrm{x}=24 \\ \mathrm{So},\mathrm{other}\mathrm{number}=24 \end{gathered}$$