Finite Math Examples

$- 2$ , $- 4$ , $- 8$ , $- 16$

Step 1

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 2

Since the LCM is the smallest positive number, $LCM (- 2, - 4, - 8, - 16) = LCM (2, 4, 8, 16)$

Step 3

Since $2$ has no factors besides $1$ and $2$ .

$2$ is a prime number

Step 4

$4$ has factors of $2$ and $2$ .

$2 \cdot 2$

Step 5

The prime factors for $8$ are $2 \cdot 2 \cdot 2$ .

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Step 5.1

$8$ has factors of $2$ and $4$ .

$2 \cdot 4$

Step 5.2

$4$ has factors of $2$ and $2$ .

$2 \cdot 2 \cdot 2$

Step 6

The prime factors for $16$ are $2 \cdot 2 \cdot 2 \cdot 2$ .

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Step 6.1

$16$ has factors of $2$ and $8$ .

$2 \cdot 8$

Step 6.2

$8$ has factors of $2$ and $4$ .

$2 \cdot 2 \cdot 4$

Step 6.3

$4$ has factors of $2$ and $2$ .

$2 \cdot 2 \cdot 2 \cdot 2$

Step 7

Multiply $2 \cdot 2 \cdot 2 \cdot 2$ .

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Step 7.1

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 2$

Step 7.2

Multiply $4$ by $2$ .

$8 \cdot 2$

Step 7.3

Multiply $8$ by $2$ .

$16$