If "M" is greater than 10?

If your "M" is > 10 and a standard 3xBB raise would push you below 10, then do you just push all-in?

Honestly I think it depends. I mean if the stack sizes on your table are so large that you have no equity then yeah, shove. Say the blinds are 500/1000 and you have 17k and the average stack at your table is 25k, i'd say that you have some fold equity and you should play your hand for value. In the latter instance I would rather try the stop and go method. I think the strength of your had dictates what you should do as well. I mean, you are gonna want to play QQ and up for value.

So, I guess in short, I think your question is a little too general and I'm gonna sit on the "it depends" fence. Then again, I'm probably wrong, I usually am.

it wouldn't! "m" is the size of your stack divided by the by the total blinds and antes. if you have an "m" of 10 then you have at least 15BBs which is enough to make a normal 3xBB raise and not be committed. having said that you should maybe making a smaller 2.5xBB raise at this point. also at this point you shouldn't be making a raise too often if it's your plan to fold to a reraise. but at the 15BBs range i start considering shoving with some hands especially if I'm out of position. there is nothing worse than holding a hand like AK making a raise only to have someone behind you flat call and then you mis the flop as you will 2/3 of the time.

i misread the question but my answer would be no. but there would be excecptions. pending on position hands strength and well well my hand does hot or cold.

Pushing with an M of 10 is a big overbet. Dan Harrington recommends an M of 5 or 6 before you go all-in. I'm guessing you meant that you had something like 11 or 12 big blinds, so raising will put you at about 9 big blinds. With antes, that has you at about an M of about 6 which is in acceptable pushing range.

But I think you are thinking to precisely.
An M of 10 is an estimate, and you shouldn't play it robotically like that. Depending on the situation (the action before you, and the likely action behind you, all based on their previous plays and current chip stacks, and possibly the payout situation as well) you can shove with your mediocre hands when you're down to an M of 4 or 5 or 6 or 7. Maybe even 3.
It's situational.

This is what I was looking for.
I find myself in those situations quite often when I make it deep in a tourney.
BTW, When you have to push and your first in vigorish, what would be your lowest pushing range from EP, MP, LP?

Harrington on Hold'em Volume 2 covers this nicely. I recommend reading Harrington on Hold'em Volume 1 and Volume 2 as they'll do a better job explaining than I will.

With an M of 5, assuming nobody has VP$IP'd into the pot, at a full table...
Early on I'll shove T/J+, 8/9s+, and any pair.
On the button I'll shove any two cards if the blinds are short too. Otherwise, any Face/rag, any pair, any connectors.

Of course, the situation varies depending on the likelihood of being called. People with middle stacks will be hurt pretty badly if they call my shove, and they are comfy with their stacks, so they are far less likely to call if I shove. People with an M of 2 or so are apt to call with anything, as are big stacks, so I shove against their blinds with a tighter range.

How active I've been (my image) and how eager to call the field has been will also effect that range.

One thing Harrington says in the book that stuck with me was that shoving with an M of 5 and winning gets you a stack of chips that have potential. So even if you're 40% to win, it's worth taking that risk for them. 40% isn't all bad, and you win that a significant number of times. If you fold a couple rounds and are down to an M of 2.5, well, even if you go in as a 60% favorite and win you only get back to an M of 5 which is still desperate/shove-and-pray time.