The product of the greatest common divisor ($G$.$C$.$D$.) and the least common multiple ($L$.$C$.$M$.) of two positive integers $a$ and $b$ is equal to: (where $a, b \in N$)

Prove that,if $a$ and $b$ are odd positive integers,then $a^{2} + b^{2}$ is even but not divisible by $4$.

The last digit of $2^{9} \cdot 5^{135}$ is ..............

State whether the following rational number has a terminating decimal expansion or not. If it does,find it: $\frac{19}{8}$

Find the square root of $30-2 \sqrt{56}$.

On a morning walk,three persons step off together and their steps measure $40\, cm$,$42\, cm$ and $45\, cm$,respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? (in $cm$)