I studied Japanese for about 2 years (and was an exchange student in Fukuoka when I was in high school) so my Japanese is rusty - but good enough to notice some interesting similarities in my Korean studies!
Of course, a lot of it is because both languages rely on Chinese characters in the beginning, and that Japan colonized Korea for a few decades, but I still find the similarities really fun!
する (su-ru) is one of the first verbs you learn in Japanese (it means "to do")
하다 (ha-da) is one of the first verbs you learn in Korean, and it means the same thing!
Check out these verbs that are almost exactly the same in Korean and Japanese:
To cook: よりする (yo-ri-su-ru) // 요리하다 (yo-ri-ha-da)
To drive: うんどうする (oon-dou-su-ru) // 운동하다 (oon-dong-ha-da)
Library: としょかん (to-sho-kan) // 도서관 (do-seo-kwan)
Part-Time Job: アルバイト (a-ru-ba-i-to) // 아르바이트 (a-reu-ba-i-teu)
Bread: パン (pan) // 빵 (bbang)
And of course, Japanese foods translate almost directly!
Ramen: らんめん (ra-men) //라면 (ra-myeon)
Udon: うどん (u-don) //우동 (u-dong)
Donkatsu: どんかつ (don-ka-tsu) // 돈까스 (don-kka-seu)
Tofu: とふ (to-fu) // 두부 (doo-boo)