From 20 natural numbers from 1 to 20, find out two numbers so that their product can be divisible by 12. Such numbers have______ Yes

From 20 natural numbers from 1 to 20, find out two numbers so that their product can be divisible by 12. Such numbers have______ Yes

12 = 2 × 2 × 3, the product of two numbers a and B should contain factor 12, which has the following possibilities: ① a = 1, B = 12, there is a pair; ② a = 2, 10, 14, B = 6, 12, 18, there are 3 + 2 + 1 = 6 pairs; ③ a = 3, 9, 15, B = 4, 8, 12, 16, 20, there are 5 + 3 + 2 = 10 pairs; ④ a = 4, 8, 16, 20, B = 3, 6, 9, 12, 15, 18, there are 5 + 4 + 1 = 10 pairs; ⑤ a = 5, 7, 11, 13, 17, 19, B = 12, there are 1 + 1 = 3 pairs; ⑥ a = 6 , 18, B = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, there are 7 + 1 = 8 pairs; ⑦ a = 12, B = 1 ~ 20, there are 8 pairs; therefore, there are 1 + 6 + 10 + 10 + 3 + 8 + 8 = 46 pairs; therefore, there are 46 pairs of such numbers

In the number that can be divided by 20 and 15, the largest one is (); in the number that can be divided by 5 and 12, the smallest one is ()

Among the numbers that can divide 20 and 15, the largest one is (5);
That is to find the greatest common divisor of 15 and 20
The smallest number that can be divided by both 5 and 12 is (60)
That is to find the least common multiple of 5 and 12