设 [tex=11.5x1.357]oVr3Dwq4mCJpVeSnaB2gBYn588roqHvJQ6B1vDe4iC6jR82S3PDAA+TMPYbEUZIrEiIVGqEDA8XkGu4Lw7Jnsw==[/tex] 叫 [tex=4.0x1.357]9L2r5tlh3JJ32yY4a6m3XQ==[/tex] 的最小公倍式，如果 [tex=2.286x1.357]HxUS4unjMZ7LUMG9lUPU+w==[/tex] 满足下面条件: [p=align:center][tex=10.0x1.357]znmn8uhEpIOGBaBK/8luaBvg4xvkvloNm5D43BuRseQ=[/tex]；[p=align:center]若 [tex=8.357x1.357]cGs6RV5vx4PqzLaofgwyg3MdFXpERxVgU3JtH4CjmDc=[/tex]，则 [tex=5.0x1.357]7JRPrTZ5cY+JHEAJlOHbeo1FIPHwzvKYg3+riOn9OhE=[/tex].试证1) [tex=4.0x1.357]9L2r5tlh3JJ32yY4a6m3XQ==[/tex] 的最小公倍式存在，且除一个非零常数因子外是唯一的.2) 以 [tex=4.714x1.357]hvdzEuFkEvrNjuF8e4Z/2g==[/tex] 表示 [tex=4.0x1.357]9L2r5tlh3JJ32yY4a6m3XQ==[/tex] 的首项系数为 1 的最小公倍式. 若 [tex=4.0x1.357]uqDWScnWkSvkvRlI8/me5Q==[/tex] 都是首一的，则 [tex=13.714x1.357]qMvPpULJ97zAJypXQBzUq7qMd5OEivHSGute6mdALS1/AqMP7XYCHfmmm2T9xrQe[/tex].3) 设 [tex=27.0x2.857]5l/0thrdJPIuGqmiJZ0yE+tMD4VzzS4vd2IYuZ8zUrkUkJsF/foSG8UDxNpVl5yTc6lRl5ts5/XehvGKwUS7UUCn+dUREMdP0wzzrLiW+0AeueyH/Q1N7SL7QfGK9oo31bptK4MrAlvMiYNbtLTQp3fJcK7KE3xVxBcpWd2RK091KOup9yJGOOmrtRtNkI/GYTa/NnIJ0NH4UCp0YVmEbA==[/tex] 为 [tex=4.0x1.357]uqDWScnWkSvkvRlI8/me5Q==[/tex] 的标准分解，则[tex=13.714x2.857]86eOesvSLJzo0xGCqVDGZpWEvgWbx0PtdAy64J142SlsYxRJS6N1AHmvUmxVytJq//ezHmpysMFuBzjaNuuDoeDOSWhbqbqtFsif98Zvkus=[/tex].