Finite Math Examples

$5 % \cdot 2000$

Step 1

Multiply each number by

$100$ to get rid of decimals.

$10000$

Step 2

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 3

The prime factors for

$10000$ are

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ .

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Step 3.1

$10000$ has factors of

$2$ and

$5000$ .

$2 \cdot 5000$

Step 3.2

$5000$ has factors of

$2$ and

$2500$ .

$2 \cdot 2 \cdot 2500$

Step 3.3

$2500$ has factors of

$2$ and

$1250$ .

$2 \cdot 2 \cdot 2 \cdot 1250$

Step 3.4

$1250$ has factors of

$2$ and

$625$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 625$

Step 3.5

$625$ has factors of

$5$ and

$125$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 125$

Step 3.6

$125$ has factors of

$5$ and

$25$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 25$

Step 3.7

$25$ has factors of

$5$ and

$5$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 4

Multiply

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ .

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Step 4.1

Multiply

$2$ by

$2$ .

$4 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 4.2

Multiply

$4$ by

$2$ .

$8 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 4.3

Multiply

$8$ by

$2$ .

$16 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 4.4

Multiply

$16$ by

$5$ .

$80 \cdot 5 \cdot 5 \cdot 5$

Step 4.5

Multiply

$80$ by

$5$ .

$400 \cdot 5 \cdot 5$

Step 4.6

Multiply

$400$ by

$5$ .

$2000 \cdot 5$

Step 4.7

Multiply

$2000$ by

$5$ .

$10000$

Step 5

Since we multiplied by

$100$ to get rid of the decimals, divide the answer by

$100$ .

$100$