Finite Math Examples

3

$3$ ,

5

$5$ ,

8

$8$ ,

11

$11$ ,

13

$13$

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

3

$3$ has no factors besides

1

$1$ and

3

$3$ .

3

$3$ is a prime number

Step 3

Since

5

$5$ has no factors besides

1

$1$ and

5

$5$ .

5

$5$ is a prime number

Step 4

The prime factors for

8

$8$ are

2 \cdot 2 \cdot 2

$2 \cdot 2 \cdot 2$ .

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Step 4.1

8

$8$ has factors of

2

$2$ and

4

$4$ .

2 \cdot 4

$2 \cdot 4$

Step 4.2

4

$4$ has factors of

2

$2$ and

2

$2$ .

2 \cdot 2 \cdot 2

$2 \cdot 2 \cdot 2$

2 \cdot 2 \cdot 2

$2 \cdot 2 \cdot 2$

Step 5

Since

11

$11$ has no factors besides

1

$1$ and

11

$11$ .

11

$11$ is a prime number

Step 6

Since

13

$13$ has no factors besides

1

$1$ and

13

$13$ .

13

$13$ is a prime number

Step 7

The LCM of

3, 5, 8, 11, 13

$3, 5, 8, 11, 13$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13

$2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13$

Step 8

Multiply

2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13

$2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13$ .

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Step 8.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13

$4 \cdot 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13$

Step 8.2

Multiply

4

$4$ by

2

$2$ .

8 \cdot 3 \cdot 5 \cdot 11 \cdot 13

$8 \cdot 3 \cdot 5 \cdot 11 \cdot 13$

Step 8.3

Multiply

8

$8$ by

3

$3$ .

24 \cdot 5 \cdot 11 \cdot 13

$24 \cdot 5 \cdot 11 \cdot 13$

Step 8.4

Multiply

24

$24$ by

5

$5$ .

120 \cdot 11 \cdot 13

$120 \cdot 11 \cdot 13$

Step 8.5

Multiply

120

$120$ by

11

$11$ .

1320 \cdot 13

$1320 \cdot 13$

Step 8.6

Multiply

1320

$1320$ by

13

$13$ .

17160

$17160$

17160

$17160$