Long term capital gains payment tiers

When paying taxes on LTCG do you pay tax % amounts for each tier level you cross into or does all of the LTCG just fall into one % bracket?

 

My Situation :

Standard  Income - $7,375.  

LTCG - 136,333.  

Total income - $143,708

Standard Deduction - $24,400

Income After Deduction - $119,308

 

Standard income falls into the 10% tax bracket. 

Combined after standard deduction falls into the 15% LTCG tax bracket.

 

The LTCG  0% bracket is $0 - 78,750

 15% bracket is $78,751 - $488,850

So do I take the 119,308  and pay only 15% on only $40,558 because that’s all that crossed over into the 15% bracket?  Or is there not cross over and I ha e to pay the 15% on the whole 119,308?  Based on my standard income I figured this would be an easy return to do next April, but maybe I’m wrong.?