解：设[tex=5.786x1.214]3TMqSL3ShOrUOCxOZTDd7Ag82k7FOhEnkTdfEJwsPog=[/tex]分别表示能被2、3、5、7整除的整数的集合，则有[tex=8.357x1.357]pvSUKheU85qZltRx/GbeOlXS/d8uDoiftN/dP2rTVQXdKNLlNWC0NhxKNKDnLiNc/4hHDtIL4rJQs0nlzE2r0w==[/tex][tex=25.357x1.357]WpTk5fPP3MtB8X87bKvf2jUzWmLx37mFNHg8YbqR1XmSNJj7pgZcHC40X42/fUQyYeKw8K+curPmL3rQq94lpreHPcBloGbZV6U/CvPUtQAGA2TNvR2QaAYU+6ItnvYD5F9QMct5XwlN80GuNzI4RQ==[/tex][tex=21.071x1.357]bR9agDzRG9LDh3pqFg+hNSz5gbWBpf91fOj7qodS/QojGwOxsnKyCmEuM/1e5ox7SevH/m1CAB8FS7j5r1FANl7WOsEbG5kWMUCJm0zJZdmuln9oU/6oNYH9iIFDb8PY99C5ciritH0yf0NU5+huuVlCDvMCvz84ouwNSD4jZ1+TzPGaUQGaURlFMl8tMOh3[/tex][tex=17.143x1.357]bXJVTS44SSwNQFinukfPU+QYLNkKsj3764JD5yyeqsjjybVRv5JCgujKQttwJ56aVMssRzv+2xO7uYFr6UGI8Q88cNUvLFT7lz+ReBRwEwDJPUhPXje0fhUv7UY7K2MZ[/tex][tex=13.643x1.357]jfoqg2s9KKN8xGYsUALOpWEsd/rFQBE9bnT17XpFllGBJCN/PEeO8sc5xlS8D4VuSG41ZkYzPeUPEivfhqpV58cTpWzj0i1tzwsP/BGzEBY=[/tex]上式中各项分别计算如下：[tex=4.143x1.357]XBKLsLFrvi/Ik4Qc/ergcLsQGxhAHhu2dgB9eSxBORk=[/tex]，[tex=3.643x1.357]8xhcXUuFoet+CR+6ri2RWXI8mEhD/O8Js6KLjFWN0/c=[/tex]，[tex=3.643x1.357]kLsuQ53qg7oeW1LAupB2pkhgyEnL/yiJq60s/Y5lxdU=[/tex]，[tex=3.643x1.357]Qr+nGVtvffSUYJPlpAJPKePs/HGbkdsFOnZJawPGe/w=[/tex]；[tex=5.857x1.357]JiTLdyXG29rgS5HbhiRzEKq4AkaENfSghXf/732gwzjXIgAFstvIRoRB8WH8N+ng[/tex]，[tex=5.5x1.357]5aNdKJQlLocpIy5RI5Ov+KNqWWaCIYsehQIgvRsdR9c=[/tex]，[tex=5.857x1.357]JiTLdyXG29rgS5HbhiRzEDl6SoYOvrg6hR7+Y5oIaEjdj3LocljV0QQhwOC6v10O[/tex]，[tex=5.857x1.357]bR9agDzRG9LDh3pqFg+hNeuif5/HkUBSUrU8SMtj9geWE+HHqfe5CW9zkWGUR9I4[/tex]，[tex=5.857x1.357]bR9agDzRG9LDh3pqFg+hNTe1M8DrbPjyFUJxRPgvuEkBy7uLCra+VLjHjhogfee+[/tex]，[tex=6.0x1.357]mOEWdJKrOPV4LVqVgoITU3stB4cSM551db0zeVzLz30=[/tex]；[tex=15.643x1.357]JiTLdyXG29rgS5HbhiRzEMA5qwFmtlyP1EGBqk1wiYRCjH4zeAbyWePFGMYQwv7oDYKmeid6qjplpuAKJmCQ0dSPcJcJKfewOZsp2a5sqDhxDFN+sIfllN5UyyVtz/Fs[/tex]，[tex=7.571x1.357]JiTLdyXG29rgS5HbhiRzEDatbC85mIcAFZM35Lz/RVGY/UDYjP5DI+USse5ZGzf3[/tex]，[tex=7.571x1.357]bR9agDzRG9LDh3pqFg+hNZvUkrORPP/O9kHpe2jWTcQbDpTL99gRPsQm7awee1W3[/tex]；[tex=9.786x1.357]JiTLdyXG29rgS5HbhiRzEMA5qwFmtlyP1EGBqk1wiYRgmjwXVC4I6LURnRmY58IWntopxjZcphD4EP4mzTIw4w==[/tex][br][/br]把以上数值代入得：[tex=10.786x1.357]pvSUKheU85qZltRx/GbeOlXS/d8uDoiftN/dP2rTVQXdKNLlNWC0NhxKNKDnLiNcmGDqIs0J4cEX4GEP3sYQZQ==[/tex]所以在1到250之间能被2、3、5、7任何任一数整数的整数个数为193。