Finite Math Examples

221 (4)

$221 (4)$ ,

131 (4)

$131 (4)$

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

The prime factors for

884

$884$ are

2 \cdot 2 \cdot 13 \cdot 17

$2 \cdot 2 \cdot 13 \cdot 17$ .

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Step 2.1

884

$884$ has factors of

2

$2$ and

442

$442$ .

2 \cdot 442

$2 \cdot 442$

Step 2.2

442

$442$ has factors of

2

$2$ and

221

$221$ .

2 \cdot 2 \cdot 221

$2 \cdot 2 \cdot 221$

Step 2.3

221

$221$ has factors of

13

$13$ and

17

$17$ .

2 \cdot 2 \cdot 13 \cdot 17

$2 \cdot 2 \cdot 13 \cdot 17$

2 \cdot 2 \cdot 13 \cdot 17

$2 \cdot 2 \cdot 13 \cdot 17$

Step 3

The prime factors for

524

$524$ are

2 \cdot 2 \cdot 131

$2 \cdot 2 \cdot 131$ .

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Step 3.1

524

$524$ has factors of

2

$2$ and

262

$262$ .

2 \cdot 262

$2 \cdot 262$

Step 3.2

262

$262$ has factors of

2

$2$ and

131

$131$ .

2 \cdot 2 \cdot 131

$2 \cdot 2 \cdot 131$

2 \cdot 2 \cdot 131

$2 \cdot 2 \cdot 131$

Step 4

The LCM of

884, 524

$884, 524$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

2 \cdot 2 \cdot 13 \cdot 17 \cdot 131

$2 \cdot 2 \cdot 13 \cdot 17 \cdot 131$

Step 5

Multiply

2 \cdot 2 \cdot 13 \cdot 17 \cdot 131

$2 \cdot 2 \cdot 13 \cdot 17 \cdot 131$ .

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 13 \cdot 17 \cdot 131

$4 \cdot 13 \cdot 17 \cdot 131$

Step 5.2

Multiply

4

$4$ by

13

$13$ .

52 \cdot 17 \cdot 131

$52 \cdot 17 \cdot 131$

Step 5.3

Multiply

52

$52$ by

17

$17$ .

884 \cdot 131

$884 \cdot 131$

Step 5.4

Multiply

884

$884$ by

131

$131$ .

115804

$115804$

115804

$115804$