Maximum common factor and minimum common multiple of 30 and 105

30 and 105 The greatest common divisor is 15, and the least common multiple is 2 10.

Common divisor, also called "common factor" It is an integer divisible by several integers at the same time.

If an integer is a divisor of several integers, it is called their "common divisor"; The greatest common divisor is called greatest common divisor. The method of finding the greatest common divisor of two numbers, multiple relation, if the larger number is a multiple of the smaller number, then the smaller number is the greatest common divisor of these two numbers.

Common multiples refer to two or more natural numbers. If they have the same multiples, then these multiples are their common multiples.

Common multiple difficulties:

The teaching emphasis of finding the least common multiple of three numbers is to let students learn the method of finding the least common multiple of three numbers, and the difficulty is to let students understand the composition of the least common multiple of three numbers, that is, the multiplication of prime factors shared by three numbers and two numbers and their unique prime factors.

This difficulty is not easy to break through. In the usual teaching, it is often seen that most teachers avoid teaching difficulties, just tell students how to find the least common multiple in the traditional "monologue" way, and then let students master this method skillfully through consolidation exercises.

In this process, students' learning is passive and their thinking is not fully activated. Real education is not a direct "telling", but meaningful knowledge that students independently construct through activities and experiences in specific situations.