Finite Math Examples

$250 \cdot 1.5$ , $375 \cdot 250$

Step 1

Multiply each number by $10$ to get rid of decimals.

$3750, 937500$

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 $3750$ are $2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ .

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Step 3.1

$3750$ has factors of $2$ and $1875$ .

$2 \cdot 1875$

Step 3.2

$1875$ has factors of $3$ and $625$ .

$2 \cdot 3 \cdot 625$

Step 3.3

$625$ has factors of $5$ and $125$ .

$2 \cdot 3 \cdot 5 \cdot 125$

Step 3.4

$125$ has factors of $5$ and $25$ .

$2 \cdot 3 \cdot 5 \cdot 5 \cdot 25$

Step 3.5

$25$ has factors of $5$ and $5$ .

$2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 4

The prime factors for $937500$ are $2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ .

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Step 4.1

$937500$ has factors of $2$ and $468750$ .

$2 \cdot 468750$

Step 4.2

$468750$ has factors of $2$ and $234375$ .

$2 \cdot 2 \cdot 234375$

Step 4.3

$234375$ has factors of $3$ and $78125$ .

$2 \cdot 2 \cdot 3 \cdot 78125$

Step 4.4

$78125$ has factors of $5$ and $15625$ .

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 15625$

Step 4.5

$15625$ has factors of $5$ and $3125$ .

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 3125$

Step 4.6

$3125$ has factors of $5$ and $625$ .

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 625$

Step 4.7

$625$ has factors of $5$ and $125$ .

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 125$

Step 4.8

$125$ has factors of $5$ and $25$ .

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 25$

Step 4.9

$25$ has factors of $5$ and $5$ .

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 5

Multiply $2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ .

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Step 5.1

Multiply $2$ by $2$ .

$4 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 5.2

Multiply $4$ by $3$ .

$12 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 5.3

Multiply $12$ by $5$ .

$60 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 5.4

Multiply $60$ by $5$ .

$300 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 5.5

Multiply $300$ by $5$ .

$1500 \cdot 5 \cdot 5 \cdot 5 \cdot 5$

Step 5.6

Multiply $1500$ by $5$ .

$7500 \cdot 5 \cdot 5 \cdot 5$

Step 5.7

Multiply $7500$ by $5$ .

$37500 \cdot 5 \cdot 5$

Step 5.8

Multiply $37500$ by $5$ .

$187500 \cdot 5$

Step 5.9

Multiply $187500$ by $5$ .

$937500$

Step 6

Since we multiplied by $10$ to get rid of the decimals, divide the answer by $10$ .

$93750$