Question

Find the smallest number which when divided by $18,12$and $24$ leaves remainder $16,10$and $22$ respectively.

Answer 1

Step 1: Find L.C.M. of $18,12,24$

L.C.M. of $18,12,24$ $=2\times 2\times 2\times 3\times 3=72$

Step 2: Finding the required number

$$\begin{gathered} 18-16=2 \\ 12-10=2 \\ 24-22=2 \end{gathered}$$

Here the common difference is $2$, so the required number will be $2$ less than L.C.M. of $18,12,24$

$\Rightarrow 72-2=70$

Therefore, the required number is $70.$