Question
Does cutting the flowers affect the propagation? What makes the bulbs multiply?

Answer
Hi Dale,
Thanx for your question.  Actually, cutting the flowers helps save energy for the bulb.  The bulb puts a lot of energy into producing the flower and then the subsequent production of seeds.  If you remove the flower before it has a chance to set seed, you will save the plant a lot of energy that it will store for next year.  Added energy, helps the plant increase itself by forming bulblets at the base of the stem, below ground.  A 3 or 4 year old lily will often have numerous bulblets in various sizes along it's underground stem or around the bulb or both.  After 3-5 years, you can dig up the plant in the fall and separate bulbs and bulblets, especially if the plant has had a reduction in blooming which is usually due to overcrowding of bulbs.  Do not cut off the green growth as it is gathering energy from the sunlight and is storing it in the bulb for next year's growth and bloom.  Wait until the green stem starts to wilt and turn brown and then you can cut it off.  I hope this helps.
Tom