The least common multiple means that the common multiple of two or more integers is called their common multiple, and the least common multiple except 0 is called the least common multiple of these integers.
The property between the greatest common factor and the least common multiple: the product of two natural numbers is equal to the product of the greatest common factor and the least common multiple of these two natural numbers. The calculation of the least common multiple is to find all common prime factors and unique prime factors of three numbers, and finally divide them into pairwise coprime.
Characteristics of the least common multiple: only the smallest multiple has no maximum, because the multiple of two numbers can be infinite.
Characteristics of the greatest common factor: the product of two numbers has the same factor, which is the greatest common factor.
When solving the problem of the greatest common divisor and the least common multiple, the following conclusions are often used:
(1) If two natural numbers are prime numbers, then their greatest common divisor is 1, and their least common multiple is the product of these two numbers.
For example, 8 and 9 are prime numbers, so (8,9) =1,[8,9] = 72.
(2) If the larger number of two natural numbers is a multiple of the smaller number, then the smaller number is the greatest common divisor of these two numbers, and the larger number is the least common multiple of these two numbers.
For example, 18 and 3, 18 ÷ 3 = 6, so (18,3) = 3, [18,3] =18.
(3) The quotient obtained by dividing two integers by their greatest common divisor is a prime number.
For example, 8 and 14 are divided by their greatest common divisor 2, and the quotients are 4 and 7 respectively, so 4 and 7 are prime numbers.
The greatest common divisor and the least common multiple are the courses in the fifth grade of primary school, and they are very important courses in primary school mathematics learning.