Generating function of integer partitions at most m parts

Question

The generating function of partition integer with the maximum number is m is $$ \frac{x^m}{(1-x)(1-x^2)\cdots(1-x^m)} $$ It's quite easy to understand if you expand it $$ (1+x+x^2+\cdots)(1+x^2+x^4+\cdots)\cdots(x^m+x^{2m}+\cdots) $$ Because m is the maximum number, you partition must contain at least one m, as for the other number less than m, you can choose 0,1,2... As the question turn to partition an integer into at most m parts, the generating function is $$ \frac{1}{(1-x)(1-x^2)\cdots(1-x^m)} $$ I can't have an intuition.