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least1 S1 W1
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at least
a) not less than a particular number or amount : 
It will take you at least 20 minutes to get there.He had at least £100,000 in savings.
It will take you at least 20 minutes to get there.He had at least £100,000 in savings. at the (very) least (=not less than and probably much more than) It would cost $1 million at the very least.
It would cost $1 million at the very least.b) even if something better is not true or is not done : At least he didn't lie to me. I don't expect you to pay me, but you could at least cover my expenses. The house still needed a lot of work, but at least the kitchen was finished.
At least he didn't lie to me.I don't expect you to pay me, but you could at least cover my expenses.The house still needed a lot of work, but at least the kitchen was finished.c) used when you are correcting or changing something that you have just said : They all knew I was on their side. At least, that's what they said. I made everything perfectly clear - or at least I thought I did.
They all knew I was on their side. At least, that's what they said.I made everything perfectly clear - or at least I thought I did.2 used when mentioning the least extreme thing that happens, is needed etc : Computer viruses are at the very least annoying and often actually destructive.
at the (very) least
Computer viruses are at the very least annoying and often actually destructive.3
the least
a) the smallest amount : Women work in those sectors of the job market which pay the least. Which method causes the least damage to the environment?
Women work in those sectors of the job market which pay the least.Which method causes the least damage to the environment?b) used to emphasize how small something is, especially when it hardly exists at all : I haven't the least idea what you are talking about. He used to wake at the least noise.
I haven't the least idea what you are talking about.He used to wake at the least noise.c) used when you are saying what someone should do in a situation, and suggesting that they should really do more : The least you could do is give me her phone number. The least they could have given her is some money towards the rent.
The least you could do is give me her phone number.The least they could have given her is some money towards the rent.4 none at all, or not at all : I tried to convince them, but they weren't the least interested. I'm not in the least afraid of you any more. His voice was alert, not the least bit sleepy.
not the least/not in the least/not the least bit
I tried to convince them, but they weren't the least interested.I'm not in the least afraid of you any more.His voice was alert, not the least bit sleepy.5 used to show that something is worse or more serious than you are actually saying : His teaching methods were strange, to say the least.
to say the least
His teaching methods were strange, to say the least.6 something that someone is not worried about because there are other more important problems : What I looked like was the least of my problems.
the least of somebody's worries/problems/troubles/concerns
What I looked like was the least of my problems.7 used to say that you are very willing to do something or to reply to someone's thanks : I'll look after them - it's the least I can do.
it's the least I can do
spokenI'll look after them - it's the least I can do.