Low back pain is often due to our posture. The way we stand. Lower Cross Syndrome describes a muscle imbalance where you have tightness in the lower back erector spine muscle group and tightness in the hip flexors. On the other sides of the joints you have weakness in the abdominals and gluts.
The tightness on one side inhibits the ability to contract the opposing muscles. So if you stand with an anterior pelvic tilt, causing a sway back, it's very difficult to correctly use your abdominals.
So while it is important to work on your core, it's even more important to stretch the hip flexors and correct the way you stand.