This is math not history.
A least common multiple (A.K.A LCM) is the smallest multiple that's divisible between two (or more)numbers.
So let's take 2 and 3 for an example. The smallest multiple that's divisible between 2 and 3 is 6.
Let's take 4 and 2 as an example. The smallest multiple that's divisible by 4 and 2, is 4.
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The greatest common factor (A.K.A GCF) is the biggest factor between 2 (or more) numbers.
Let's take 6 and 3 as an example.
The factors of 6 are 1, 2, 3, 6.
Factors of 3: 1, 3.
So the GCF is 3.
Let's take 8 and 20
20's factors: 1, 2, 4, 5, 10, 20
8's factors: 1, 2, 4, 8.
Therefore, the GCF is 4.