The British had suffered 420,000 casualties. The French lost nearly 200,000 and it is estimated that German casualties were in the region of 500,000.That was one battle. American casualties in all of World War II were about the same as Britain's for the Battle of the Somme.
I think that too many Europeans use the two world wars as an excuse to evade responsibility for security today (foot-dragging on Yugoslavia is the best example), but just as many Americans fail to appreciate how the effects of two absolutely devastating wars in the first half of the twentieth century have filtered down throughout Europe. Imagine the Civil War had been followed up 20 years later with an even deadlier, more destructive war and then imagine how gun shy America might have been throughout the first half of the twentieth century.