Finite Math Examples

3

$3$ ,

225

$225$

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

The prime factors for

225

$225$ are

3 \cdot 3 \cdot 5 \cdot 5

$3 \cdot 3 \cdot 5 \cdot 5$ .

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Step 3.1

225

$225$ has factors of

3

$3$ and

75

$75$ .

3 \cdot 75

$3 \cdot 75$

Step 3.2

75

$75$ has factors of

3

$3$ and

25

$25$ .

3 \cdot 3 \cdot 25

$3 \cdot 3 \cdot 25$

Step 3.3

25

$25$ has factors of

5

$5$ and

5

$5$ .

3 \cdot 3 \cdot 5 \cdot 5

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

3 \cdot 3 \cdot 5 \cdot 5

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

Step 4

Multiply

3 \cdot 3 \cdot 5 \cdot 5

$3 \cdot 3 \cdot 5 \cdot 5$ .

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Step 4.1

Multiply

3

$3$ by

3

$3$ .

9 \cdot 5 \cdot 5

$9 \cdot 5 \cdot 5$

Step 4.2

Multiply

9

$9$ by

5

$5$ .

45 \cdot 5

$45 \cdot 5$

Step 4.3

Multiply

45

$45$ by

5

$5$ .

225

$225$

225

$225$