WEBVTT 00:00:00.700 --> 00:00:03.130 小吴和小刘 00:00:03.130 --> 00:00:04.370 在思睿学校不同的班级上物理课。 00:00:04.370 --> 00:00:07.750 小刘的老师总是在每次考试时出30道题， 00:00:07.750 --> 00:00:10.870 而小吴的老师考试更加频繁， 00:00:10.870 --> 00:00:14.150 但每次考试出24道题。 00:00:14.150 --> 00:00:17.802 小刘的老师每年还要布置3个专题项目。 00:00:17.802 --> 00:00:20.260 尽管这两个班考试的次数不一样， 00:00:20.260 --> 00:00:22.270 他们的老师告诉他们， 00:00:22.270 --> 00:00:25.250 两个班级，让我们画上重点线， 00:00:25.250 --> 00:00:29.040 两个班每年考试题目的总数量必须相同。 00:00:29.040 --> 00:00:32.850 那么，小吴和小刘的两个班 00:00:32.850 --> 00:00:36.807 每年考试题目总数的最小值应该是多少？ 00:00:36.807 --> 00:00:38.390 现在我们来看，这道题是什么意思。 00:00:38.390 --> 00:00:40.014 小刘的老师每次 00:00:40.014 --> 00:00:44.590 出30道题，所以第一次考试之后， 00:00:44.590 --> 00:00:46.850 他做了30题。 00:00:46.850 --> 00:00:48.750 这里是0， 00:00:48.750 --> 00:00:52.240 第二次考试之后，他就做过60道题。 00:00:52.240 --> 00:00:56.150 第三次考试之后，他就做过90道题。 00:00:56.150 --> 00:01:00.070 第四次考试之后，他就做过120道题。 00:01:00.070 --> 00:01:03.480 第五次考试之后，如果有的话， 00:01:03.480 --> 00:01:06.700 他就做过--如果真是考了这么多次-- 00:01:06.700 --> 00:01:08.912 他就做过150道题。 00:01:08.912 --> 00:01:10.620 我们可以这样一直继续下去， 00:01:10.620 --> 00:01:12.467 来寻求所有30的倍数。 00:01:12.467 --> 00:01:14.800 这或许是我们考虑问题的一个线索。 00:01:14.800 --> 00:01:16.549 我们在寻找一个数的倍数。 00:01:16.549 --> 00:01:19.710 我们在寻找最小的倍数。 00:01:19.710 --> 00:01:20.950 这是小刘的情况。 00:01:20.950 --> 00:01:22.710 现在，我们再来看小吴是什么情况？ 00:01:22.710 --> 00:01:25.650 小吴的老师，在第一次考试之后， 00:01:25.650 --> 00:01:29.220 让他们做了24道题， 00:01:29.220 --> 00:01:32.770 然后，第二次考试后，他们就会做48道题， 00:01:32.770 --> 00:01:37.420 第三次考试之后，他们就会做72道题。 00:01:37.420 --> 00:01:39.250 然后，他们会做96道题， 00:01:39.250 --> 00:01:41.820 我只看24的倍数。 00:01:41.820 --> 00:01:45.030 在第四次考试后，他们会做96道题。 00:01:45.030 --> 00:01:49.610 在第五次考试之后，他们就会做过120道题。 00:01:49.610 --> 00:01:55.160 如果有第六次考试，他们就会做过144道题。 00:01:55.160 --> 00:01:57.430 这样，我们可以一直继续下去。 00:01:57.430 --> 00:01:58.300 但是，我们来看，题目怎么问的， 00:01:58.300 --> 00:02:00.180 小吴和小刘在一年里 00:02:00.180 --> 00:02:03.200 做过的题目数相同的数里面，最小的那个是什么？ 00:02:03.200 --> 00:02:04.710 好， 最小的数就是这个点。 00:02:04.710 --> 00:02:07.380 在这里，我们得到了相同的考试题目数。 00:02:07.380 --> 00:02:09.190 尽管每次考试的题目数 00:02:09.190 --> 00:02:10.617 是不同的， 00:02:10.617 --> 00:02:12.950 你们可以看到，在这里，他们得到相同的数。 00:02:12.950 --> 00:02:14.880 它是120. 00:02:14.880 --> 00:02:16.770 在120 这一点， 00:02:16.770 --> 00:02:19.300 他俩都做了120道题。 00:02:19.300 --> 00:02:21.840 尽管小刘的老师每次考试出30题， 00:02:21.840 --> 00:02:25.240 而小吴的老师每次出24题。 00:02:25.240 --> 00:02:28.469 所以，答案就是120. 00:02:28.469 --> 00:02:30.510 注意，他们考试的次数不一样， 00:02:30.510 --> 00:02:33.650 小刘考了1，2，3，4次试， 00:02:33.650 --> 00:02:36.300 而小吴考了1，2，3，4， 00:02:36.300 --> 00:02:37.570 5次试。 00:02:37.570 --> 00:02:41.270 但他们做题的总数都是120道题。 00:02:41.270 --> 00:02:44.100 现在，我们用数学方式来表达。 00:02:44.100 --> 00:02:47.370 00:02:47.370 --> 00:02:55.650 00:02:55.650 --> 00:02:56.980 00:02:56.980 --> 00:03:02.692 00:03:02.692 --> 00:03:04.150 00:03:04.150 --> 00:03:06.399 00:03:06.399 --> 00:03:07.870 00:03:07.870 --> 00:03:10.440 00:03:10.440 --> 00:03:15.290 00:03:15.290 --> 00:03:20.420 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