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Is it significant to use short division in finding the greatest common divisor and the least common multiple in fifth grade mathematics teaching?
Not the longest common divisor, but the greatest common divisor.

Short division is the most commonly used method to find the greatest common divisor and the least common multiple, which is the same as prime factorization, but simpler than prime factorization.

Short division:

Short division is a method to find the greatest common factor and can also be used to find the least common multiple. The method of finding the greatest common factor of several numbers begins with observation and comparison, that is, first find out the factor of each number, then find out the common factor, and finally find out the greatest common factor in the common factor. After that, the factorization prime factor method is used to decompose the factors of two numbers respectively, and then the operation is carried out. Then it evolved into short division, divided by prime numbers together, and finally sorted out.

Multiply the greatest common divisor by one side and the least common multiple by one circle.