Question

Determine the smallest natural number , which when divided by $12,16,24$ leaves remainder $7$ in each case.

Answer 1

Explanation:

To find the number divisible by $12,16,24$ , we have to find the LCM.

$$\begin{gathered} 12=2\times 2\times 3 \\ 16=2\times 2\times 2\times 2 \\ 24=2\times 2\times 2\times 3 \end{gathered}$$

The LCM $=2\times 2\times 2\times 2\times 3=48$

From given information, The number leaves a remainder of $7$

So,the smallest natural number $$\begin{gathered} =48+7 \\ =55 \end{gathered}$$

Hence,the smallest number divisible by $12,16,24$ leaves a remainder $7$ will be $55$.