Xiao Ming, Xiao Wang and Xiao Li often go to the library. Xiao Ming goes every four days, Xiao Wang every five days and Xiao Li every two days. We met in the library on August 5 and met again on August 25.

Analysis: The least common multiple of 4, 5 and 2 is 20, so we met again on August 25th.

The scope of application of the least common multiple: addition and subtraction of fractions, China's remainder theorem (the correct problem has a solution and a unique solution within the least common multiple). Because prime numbers are numbers that cannot be divisible by numbers other than 1 and their own numbers.

The n power of prime number X can only be divisible by the n power and the lower power of X, 1 and its own number. So give a definition of the least common multiple: the least common multiple of the S number is the product of the highest power of the prime factor contained in this S number.

Interpretation of nature and characteristics

The nature of the least common multiple: the common multiple means that if two or more natural numbers have the same multiple, these multiples are their common multiples, and the least common multiple except 0 is called the least common multiple of these numbers.

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.