What is the difference between a common multiple and a common factor?

The common multiple is any common multiple between them; The common factor is any common factor between them.

The smallest common multiple is between all their common multiples, and the smallest 1, such as the common multiple of 3 and 6, is 6. The lowest common factor is the smallest of them 1. For example, the least common factor of 3 and 6 is 3. The greatest common multiple is the largest1; The greatest common factor is the smallest 1.

Decomposition prime factor method

First, write down the prime factors of two numbers, and the least common multiple is equal to the product of the representatives of the prime factors shared by all two numbers and their unique prime factors.

For example, find the least common multiple of 45 and 30. 45=3×3×5,30=2×3×5。

The common prime factors of 30 and 45 are 1 3s and 1 5s, while the unique prime factors of 30 and 45 are 3 and 2 respectively. That is, the least common multiple is equal to 2×3×3×5=90.