Charity work

Peter likes to take care of grandmothers and their well-being. Every $n$-th day he transferred old women across the road, every $k$-th he declared that the welfare of grandmothers increased, and every $m$-th day he promised that soon they would be even better. Today he did three things and was very tired, but he was very pleased.

Write a program that will determine after how many days such a meaningful day will happen, and how many boring days will happen during this period, when he will not do any of his favorite things.