1. Fill in the blanks.

1. Both are natural numbers. If the greatest common divisor of is (), the least common multiple is ().

2. The greatest common divisor of A, B, A and B is ()× () = (), and the smallest common multiple of A and B is ()× ()× () = ().

3. The common divisor of all natural numbers is ().

4. If m and n are prime numbers, then their greatest common divisor is () and their least common multiple is ().

5.4, 9, 10 and 16, of which () and () are prime numbers, () and () are prime numbers.

6. Divide 15 and 30 by a number, which is exactly divisible. The maximum quantity is ().

*7. The sum of two consecutive natural numbers is 2 1, the greatest common divisor of these two numbers is (), and the least common multiple is ().

*8. The sum of two adjacent odd numbers is 16. Their greatest common divisor is () and their least common multiple is ().

**9. When a number is divisible by 3, 5 and 7, it is 1, and the minimum number is ().

10. Write two prime numbers according to the following requirements.

(1) Two prime numbers ().

(2) Two consecutive natural numbers () and ().

(3) 1 and arbitrary natural numbers () and ().

(4) Two composite numbers () and ().

(5) Odd numbers and odd numbers () and ().

(6) Odd and even numbers () and ().

2. True or false.

1. The coprime of two numbers must be both prime numbers. ( )

2. Two different odd numbers must be prime numbers. ( )

3. The smallest prime number is the greatest common divisor of all even numbers. ( )

4. Two numbers with common divisor 1 must be prime numbers. ( )

5.a is a prime number and B is also a prime number, so it must be a prime number. ( )

3. Directly say the greatest common divisor and the least common multiple of each group number.

26 and 13() 13 and 6() 4 and 6 ()

5 and 9() 29 and 87() 30 and 15 ()

13,26 and 52 () 2,3 and 7 ()

4. Find the greatest common divisor and the least common multiple of each group of numbers below. (Only the least common multiple of three numbers)

45 and 60, 36 and 60

27 and 72, 76 and 80

42, 105 and 56 24, 36 and 48

* * 5. Think about it:

The school bought 40 ballpoint pens and 50 exercise books, which were awarded to the third-class students in grade four on average. As a result, there are four more ballpoint pens and two more exercise books. There are several third-class students in the fourth grade. What prize did they win?