You can easily make your own Play-doh at home (sweet! budget friendly). It takes about 10 minutes to mix together, an hour for it to cool, and then 10 extra minutes per color that you want because you have to knead the dye into the doh by hand. So after a couple hours you have yourself 3 to 5 colored play-doh balls and a sore hand and forearm. But the reward, oh the reward, is excellent. This amount of work will give your 15 month old approximately 120 seconds of F-U-N. Put the play-doh in a Ziploc bag and it may take your baby long enough to open the bag for you to put away a few dishes.
All you need is a little table or desk (found one for $1.50 at the thrift store, check!) and a few supplies like crayons, colored pencils, paper, tempera paint, etc. You probably won't even get as far as painting because coloring with colored pencils will keep your 15 month old occupied for so long. 20 seconds. Two marks on the page and you've got yourself a regular Picasso. Taking the colored pencils out of their case will buy your toddler a few extra seconds of play time.
If you really want to keep your 15 month old entertained, Bubbles will mesmerize him for 5 whole minutes. One minute of you showing him what to do, a couple minutes of him dipping the wand in the bubbles and then IN his mouth, and then if you're really lucky, he'll dump the bubbles all over the floor and, BAM, a few more minutes of play time splashing around in a soapy mess.
So after a few hours of prep time, a few dollars out of your pocket, and a boat-load of clean up, you can keep your 15 month old entertained for ten and a half minutes of your day.