Solution:
Let these two numbers be x and y respectively.
Because x and y are multiples of 4, let.
x = 4my = 4n
x+y = 52； that is
4m+4n = 52；
Get: m+n =13;
Induction: when m = 1; When n= 12, the least common multiple is not144; Do not meet;
When m = 2; When n= 1 1, it does not meet the requirements;
.......
When m=4 and n=9, that is, x= 16 and y=36, the sum of x and y is 52, their greatest common divisor is 4, and their smallest common multiple is 144.
Get a solution.
2. Multiply eight numbers first, and then open the square root, and get that the equal product should be 5855850. The answer unit number is 0, so in the two groups, 14 and 30 should be divided into different groups, and 14 should be divided into groups with unit number 5. Because 14 is small, you can choose 75, and the other group should choose from 14*75/30=35.
The remaining 33, 39, 143, 169 can be matched according to the size and can be divided into 33, 169 and 39, 143 groups. 33* 169=39* 143
So the answer is:14 * 75 * 33 *169 30 * 35 * 39 *143 or:14 * 75 * 39 *143 30 * 35 * 33.
3. Solution:
Bottom = length * width, right = width * height.
So the sum of the areas of the bottom surface and the right side surface is:
Width * (length+height)
Because length, width and height are prime numbers.
So first, decompose 125 into prime factors:
125=5*5*5
So: width * (length+height) =5*5*5.
In this case, the width must be 5. Otherwise, none of the other numbers are prime numbers.
So length+height =25.
Since all prime numbers except 2 are odd numbers, and the length and height are prime numbers, and the sum is 25, which are all odd numbers, it is impossible to be all odd numbers, but it must be odd and even. So the length and height are 2 and 23, respectively.
So! There is only one possibility of volume.
The length and height are 2cm and 23cm respectively, and the width is 5cm.
So the volume is: 2*23*5=230 (cubic centimeter).
4. Solve the sequence equation.
The teacher asked Xiaohu to buy X exercise books and Y pencils.
0.4x+0.32y= 10
Xiaohu confused the number of exercise books with the number of pencils.
That is, I bought y exercise books and x pencils.
It takes 10-0.56=9.44 yuan to get back 0.56 yuan.
0.32x+0.4y=9.44
Solve it
x= 17，y= 10
So the teacher originally planned to let Xiaohu buy 17 exercise books.