1) First and foremost because in the swimming I want to keep my body as much as possible parallel to the water surface in order to gain speed and I can achieve this only if I have an iron core.
2) On the bike, if you want to avoid lower back pains, it's your abdomen that should be in charge of sustaining your upper-body weight.
3) Finally, the stronger the core the better runner you’ll be. A strong core will help not only sustain the weight of your upper body but it will help you lift the legs and achieve longer strides.
That is why I train my core and abs everyday for at least 30 minutes, and I'm pretty satisfied with the results...I mean, the picture below is good proof, right?
Anyway, this is in a nutshell my core and abs routine. I do 3 (sometime 4) sets of each exercise, it's pretty intense, and at the end I can barely feel my muscles. Hope you find this useful!
Note: I posted some YouTube's videos that show how to do the exercises. I find those very useful because they teach the correct form which I believe is crucial!