A positive integer, which is not a multiple of 120 after adding 75 and 48 respectively, but the product of these two sums can be divisible by 120. What is the smallest positive integer?
一个正整数，它分别加上75和48以后都不是120的倍数，但这两个和的乘积却能被120整除．这个正整数最小是多少？
<result>117</result>