Finite Math Examples

$22$ , $15$ , $69$ , $65$ , $85$ , $74$ , $45$ , $45$ , $45$ , $22$

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

$22$ has factors of $2$ and $11$ .

$2 \cdot 11$

Step 3

$15$ has factors of $3$ and $5$ .

$3 \cdot 5$

Step 4

$69$ has factors of $3$ and $23$ .

$3 \cdot 23$

Step 5

$65$ has factors of $5$ and $13$ .

$5 \cdot 13$

Step 6

$85$ has factors of $5$ and $17$ .

$5 \cdot 17$

Step 7

$74$ has factors of $2$ and $37$ .

$2 \cdot 37$

Step 8

The prime factors for $45$ are $3 \cdot 3 \cdot 5$ .

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Step 8.1

$45$ has factors of $3$ and $15$ .

$3 \cdot 15$

Step 8.2

$15$ has factors of $3$ and $5$ .

$3 \cdot 3 \cdot 5$

Step 9

$22$ has factors of $2$ and $11$ .

$2 \cdot 11$

Step 10

The LCM of $22, 15, 69, 65, 85, 74, 45, 45, 45, 22$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 3 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \cdot 17 \cdot 23 \cdot 37$

Step 11

Multiply $2 \cdot 3 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \cdot 17 \cdot 23 \cdot 37$ .

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Step 11.1

Multiply $2$ by $3$ .

$6 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \cdot 17 \cdot 23 \cdot 37$

Step 11.2

Multiply $6$ by $3$ .

$18 \cdot 5 \cdot 11 \cdot 13 \cdot 17 \cdot 23 \cdot 37$

Step 11.3

Multiply $18$ by $5$ .

$90 \cdot 11 \cdot 13 \cdot 17 \cdot 23 \cdot 37$

Step 11.4

Multiply $90$ by $11$ .

$990 \cdot 13 \cdot 17 \cdot 23 \cdot 37$

Step 11.5

Multiply $990$ by $13$ .

$12870 \cdot 17 \cdot 23 \cdot 37$

Step 11.6

Multiply $12870$ by $17$ .

$218790 \cdot 23 \cdot 37$

Step 11.7

Multiply $218790$ by $23$ .

$5032170 \cdot 37$

Step 11.8

Multiply $5032170$ by $37$ .

$186190290$