2. Determine all the common factors and two
common multiples of 12 and 56. Show
your work.

9514 1404 393

Step-by-step explanation:

Common factors of 12 and 56 will be factors of the greatest common factor (GCF) of those numbers. That can be found several ways. One is to list the prime factors of each number, then choose the ones that are common.

  12 = 2·2·3

  56 = 2·2·2·7

The common factors are 2·2. Of course 1 is always a factor. So, "all common factors" are 1, 2, 4.

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The least common multiple (LCM) can be figured using the same lists of factors. It must include all of the factors (only as many times as necessary), so will be ...

  2·2·2·3·7 = 168

It can also be figured as the product of the two numbers, divided by their GCF:

  12·56/4 = 168

Any "common multiple" will be a multiple of this LCM. Some common multiples of 12 and 56 are ...

  1·168 = 168; 2·168 = 336; 3·168 = 504

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