Question

Find the smallest number which when divided by 4 gives a reminder 3,when divided by 3 gives reminder 2 and when divided by 2 gives reminder 1 ?

Answer 1

$$\begin{gathered} \mathrm{In}\mathrm{each}\mathrm{case}\mathrm{remainder}\mathrm{is}\mathrm{different}, \\ \mathrm{But}\mathrm{the}\mathrm{difference}\mathrm{in}\mathrm{divisor}\mathrm{and}\mathrm{remainder}\mathrm{is}\mathrm{same}=1 \\ \mathrm{So},\mathrm{required}\mathrm{least}\mathrm{no}=\mathrm{L}.\mathrm{C}.\mathrm{M}(2,3,4)-1 \\ \mathrm{Now}, \\ \mathrm{L}.\mathrm{C}.\mathrm{M}\mathrm{of}(2,3,4): \\ 2=2\times 1 \\ 3=3\times 1 \\ 4=2\times 2\times 1 \\ \mathrm{Reqd}.\mathrm{L}.\mathrm{C}.\mathrm{M}=3\times 2\times 2=12 \\ \mathrm{So},\mathrm{required}\mathrm{least}\mathrm{no}=\mathrm{L}.\mathrm{C}.\mathrm{M}(2,3,4)-1=12-1=11 \end{gathered}$$