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The shibud of Mitrayim was 116 years (Rashi Vaera 6:16 quoting Seder Olam Rabbah):
The years of Levi are counted to show the shibud did not start until the last of the brother passed on- and that was Levi.
The brothers (except for Binyamin) were born within 6 years of eachother. Subtract 2 years for Reuven and Shimon. That made Levi 4 years older than Yosef, who was the last of the six years. Yosef was 30 when he came before Paroah and Levi 34, + 7 years of sava, + 2 years of famine, making Levi 43 when he and his family arrived in Mitzrayim- the start of the 210 years. Levi was 137 when he died, making his stay in Mitzrayim 94 years and that was the start of the shibud. 210 - 94= 116.
Parshas Beshalach has 116 Pesukim
It was taught in a Baraisa in the name of R' Nechemiah: For nearly 116 years the fire was aflame in the Altar but nevertheless it's wood did not burn and it's copper did not melt...
Vayikra Rabbah 7:5