展开全部先把已知等式转换一下：A*B=6*A+6*B
---》 A=6*B/（B-6）=6+36/（B-6）从上式可以看出，要使A是自然数，则36/（B-6）必须是自然数，也就是36能整除B-6。能被36整除的自然数，有1、2、3、4、6、9、12、18、36。所以，可以逐一检验：B-6=1，则B=7，A=42B-6=2，则B=8，A=24B-6=3，则B=9，A=18B-6=4，则B=10，A=15B-6=6，则B=12，A=12，A=B，不合题意B-6=9，则B=15，A=10B-6=12，则B=18，A=9B-6=18，则B=24，A=8B-6=36，则B=42，A=7所以，共有7组答案。
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