I know they both mean "at least", unless I'm wrong.
1 Answer
"At least" is merely the English translation of the phrases found in bilingual dictionaries. It tells us nothing about how 「せめて」 and 「少なくとも」 are (and are not) used in the actual Japanese-speaking world.
In my Japanese ear, to tell the truth, 「せめて」 and 「少なくとも」 sound like two fairly different types of phrases even though I must admit that they are sometimes actually interchangeable.
「せめて」 often sounds emotion-packed. One uses it to appeal or complain for the minimum number/amount/frequency, etc. of something that one desires to have.
「少なくとも」 is more about cold numbers and such describing the minimum requirements unless other words expressing emotions are attached to it.
If a mother said 「せめて[年]{ねん}に[一度]{いちど}でもスミ[子]{こ}から[便]{たよ}りがあればねぇ。」, she would sound like she was in grief for her goofy daughter Sumiko who does not even write/call her mother once a year.
If the mother used 「少なくとも」 instead of 「せめて」, it would not sound nearly as sorrowful. She would sound as if it were okay with her if she did not hear from Sumiko very often.
Finally, an example where the two phrases can never be interchangeable:
「[東京]{とうきょう}からニューヨークまでは行くには少なくとも12[時間]{じかん}はかかる。」
The context here is all about math and science; there are no emotions involved anywhere. You could never use 「せめて」 in that sentence even if you wanted to. If you used it, the sentence would not make any sense at all to us Japanese-speakers.