Question

Find the least number which when divided by $32,64$ and $128$ leaves $8$ as the remainder. [3 Marks]

Answer 1

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

$\begin{array}{cc}2& 32,64,128\\ 2& 16,32,64\\ 2& 8,16,32\\ 2& 4,8,16\\ 2& 2,4,8\\ 2& 1,2,4\\ 2& 1,1,2\\ & 1,1,1\end{array}$

$\therefore$ LCM $=2\times 2\times 2\times 2\times 2\times 2\times 2$

L.C.M. $=128$ [2 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 L.C.M.
$\Rightarrow 128+8=136$

Hence, the least number which when divided by $32,64$ and $128$ which leaves $8$ as the remainder is $136$.
[1 Mark]