The chief advocates of the Low Carb movement would have you believe that it's all to do with Insulin.
Cancer is a metabolic disease (
Clickity) apparently; and you're much less likely to get it if you eat less (a) sugar, (3) protein, (vi) anything else.
Cancer really hates it if you combine Chemo with Fasting (
No No, click me!)
The commonality? Insulin. Chronically raised insulin is really really bad.
You can reduce it through various means; including exercise. Remember Michael Mosely on the BBC - he improved his Insulin sensitivity massively with just 3x30s of HIIT a week.
Bottom line is - if you combine a few minutes of raised heart-rate, with some moderation in your sugar-eating, doughnut-munching ways, not to mention quitting smoking, and moderating the sauce - you'll likely reduce your cancer risk by A. Lot.