Thread: at least

1. He didn't come in my birthday but he could at least phone me!
2. The President should at least respect the entitlments of the veterans.
3. In all, neighbors called at least 11 times over the past three years, flagging the same animal owners.

хотя бы - 1,2 (expressing wish of something to be done or to have some quality/quantity)
по крайней мере/как минимум - 1,2,3 (more universal, like 'at least')

Originally Posted by Alex80

хотя бы

Thanks Alex.
Он хотя бы мог позвонить мне ...
или
Он мог хотя бы позвонить мне ...

Both are correct.
However in first case "хотя бы" is applied to "мог", while in second case "хотя бы" is applied to "позвонить".
So... first one is better suitable for expressing idea, that he could make the call. It's more like satisfaction or wonderment about the fact that he has ability to do this call. Something failed to prevent him from doing this. Note, that latter doesn't implies that he really did it. Just fact of ability.
Second one is better suitable for expressing idea, that the call was the thing which he could make, but he didn't. It's more like regret or anger about fact that he didn't make call, despite of his ability to do it.

However, these things can be changed by stressings in living speech. So, context sometimes can be more important.

1. He didn't come to my birthday but he could at least phone me!
2. The President should at least respect the entitlements of the veterans.

It's probably better to say "call" instead of "phone." While it's "OK" to say "phone," it's a bit unnatural.

I am extremely tired but I must work at least one hour more in order to prepare for the tomorrow's meeting.

Я чрезмерно уставший но мне следует хотя бы работать один час больше для того чтоб приготовиться на завтрашнюю встречу

Я чрезмерно уставший но мне следует хотя бы работать один час больше для того чтоб приготовиться на завтрашнюю встречу

Я (очень) сильно уставший ("чрезмерно" is not well-suited for this role. Also "Я (очень) сильно устал" is simplier and little more natural here)
но мне надо ("следует" is more like "should", not "must")
поработать (perfect verb for complete actions)
хотя бы на один час больше.... ("one hour" should be stressed by "at least", so, move second one before first one. Also there must be joint "на" here)
для того, чтобы ("чтоб" is demotic)
приготовиться к завтрашней встрече. (готовятся "к чему либо")

More literary way to say would be "Я чрезвычайно устал, но мне придётся работать по крайней мере на один час больше, чтобы успеть приготовиться к завтрашней встрече"

Чрезмерный = "сверх всякой меры" -- is more about "over" than "high":
"От чрезмерного напряжения у него разболелась голова."