Question

Find the least number which when divided by 18,24,30 and 42 leaves the remainder1

Answer 1

$$\begin{gathered} 18=2\times 3\times 3 \\ 24=2\times 2\times 2\times 3 \\ 30=2\times 3\times 5 \\ 42=2\times 3\times 7 \\ \mathrm{So}\mathrm{LCM}=2\times 2\times 2\times 3\times 3\times 5\times 7 \\ =2520 \\ \mathrm{So}\mathrm{required}\mathrm{number}=2520+1=2521 \end{gathered}$$