How do I run the same linux command in more than one tab/shell simultaneously?

As mavillan already suggested, just use terminator. It allows to display many terminals in a tiled way. When enabling the broadcasting feature by clicking on the grid icon (top-left) and choosing "Broadcast All", you can enter the very same command simultaneously on each terminal.

Here is an example with the date command broadcasted to a grid of 32 terminals.

tmux has this capability. (along with many other useful capabilities in the same vein)

Can be done via:

:setw synchronize-panes on

It can be achieved using iTerm2

Reference: http://korishev.com/blog/2014/02/28/iterm2-broadcast-input/