Finite Math Examples

57

$57$ ,

5

$5$ ,

39

$39$

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

57

$57$ has factors of

3

$3$ and

19

$19$ .

3 \cdot 19

$3 \cdot 19$

Step 3

Since

5

$5$ has no factors besides

1

$1$ and

5

$5$ .

5

$5$ is a prime number

Step 4

39

$39$ has factors of

3

$3$ and

13

$13$ .

3 \cdot 13

$3 \cdot 13$

Step 5

The LCM of

57, 5, 39

$57, 5, 39$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

3 \cdot 5 \cdot 13 \cdot 19

$3 \cdot 5 \cdot 13 \cdot 19$

Step 6

Multiply

3 \cdot 5 \cdot 13 \cdot 19

$3 \cdot 5 \cdot 13 \cdot 19$ .

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Step 6.1

Multiply

3

$3$ by

5

$5$ .

15 \cdot 13 \cdot 19

$15 \cdot 13 \cdot 19$

Step 6.2

Multiply

15

$15$ by

13

$13$ .

195 \cdot 19

$195 \cdot 19$

Step 6.3

Multiply

195

$195$ by

19

$19$ .

3705

$3705$

3705

$3705$