(Ooops... my apologies. This is my first posting and I didn't know that as soon as I attached the first image that the posting would be submitted. Anyway, I do still want this weed identified, but this particular weed is mostly invading my landscaping beds, not my lawn.)
Thanks!

Looks like Vetch

Here is a link that might be useful: Common Vetch

noinwi -- you are "the bomb"! That's it! Thank-you so much for the help. Now that I know the name of it, I've found lots of information on it to read. Surprisingly to me, there's more information on how to grow it, than on how to kill it. Growing it must not be too difficult, since it seems to do quite a good job in my beds on its own. Have a great weekend, and thanks again for the help.
Arden