Disclaimer: Before I answer, I need to specify that age of consent is such a debate because as you want to put there's not an only answer; each continent, country and region depend of their own culture or tradition and the law is unclear with the age per se, so since you asked for age of consent and didn't clarify which act do you ask for, I'm going to answer since the legal sex and marriage view. For example (generically speaking), the age of consent to drink alcohol is 18 but you can marry at 15 years with the father's consent.
Now: the lowest age of consent in the entire world (generically speaking) is Angola. To have heterosexual sex you need to have 12 years old. According to several links I've been checking, in this country, while you can have sex with 12, most of the sex acts made and/or practiced in this age can be considered as sexual abuse and punished with 5 to 8 years of prison. Yet, you can do it, but considering some differences between their internal laws.
The Angola's Penal Code establishes punishments for people who commit sexual abuse with someone under the age of 14, the legal age for someone to have legal (forgive the repetition) heterosexual sex (Art. 179 - 184). But, to get married, according to the Civil Code the girl need to have 15 (not less) years and the male at least 16 years, with parent consent of both. (Art. 24).
Again, this question is very generic, so there won't be AN answer, there are lot of answers.