First lest find the Least Common Multiple of 13, 8 and 14

13 = 1*13

8 = 2^3

14 = 2*7

LCM (13, 8, 14) = 13*8*7 = 728

Mary caught a sea bass that weighed: 2 11/13 = 2 (11*8*7)/(13*8*7) = 2 616/728

Susan caught one that weighed: 2 17/8 = 2 (17*13*7)/(13*8*7) = 2 1547/728

Jean caught one that weighed: 2 13/14 = 2 (13*13*4)/(13*4*14) = 2 676/728

Since 1547/728 > 676/728 > 616/728 we conclude that Susan caught the heaviest sea bass.