Question

Find the least number which when divided by $32,64$ and $128$ leaves $8$ as the remainder.

Answer 1

The smallest number that is divisible by $32,64,128$ is their LCM.
We can find the LCM of $32,64,128$ by common division method as follows:

$\begin{array}{cc}2& 3264128\\ 2& 163264\\ 2& 81632\\ 2& 4816\\ 2& 248\\ 2& 124\\ 2& 112\\ & 111\end{array}$
...(1 mark)

$\therefore$ LCM $=2\times 2\times 2\times 2\times 2\times 2\times 2$ ...(0.5 marks)

LCM $=128$ ...(0.5 marks)

So, when $128$ is divided by $32,64$ and $128$ there is no remainder. So, to get the remainder as $8$ we need to add $8$ to the LCM.
$\Rightarrow 128+8=136$ ...(0.5 marks)

Hence, the least number which when divided by $32,64$ and $128$ which leaves $8$ as the remainder is $136$. ...(0.5 marks)