Finite Math Examples

$3$ , $7$ , $13$ , $19$ , $22$ , $21$ , $17$ , $10$ , $8$ , $1$ , $8$ , $13$ , $15$ , $24$ , $17$ , $13$ , $4$ , $10$ , $15$ , $20$

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 $3$ has no factors besides $1$ and $3$ .

$3$ is a prime number

Step 3

Since $7$ has no factors besides $1$ and $7$ .

$7$ is a prime number

Step 4

Since $13$ has no factors besides $1$ and $13$ .

$13$ is a prime number

Step 5

Since $19$ has no factors besides $1$ and $19$ .

$19$ is a prime number

Step 6

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

$2 \cdot 11$

Step 7

$21$ has factors of $3$ and $7$ .

$3 \cdot 7$

Step 8

Since $17$ has no factors besides $1$ and $17$ .

$17$ is a prime number

Step 9

$10$ has factors of $2$ and $5$ .

$2 \cdot 5$

Step 10

The prime factors for $8$ are $2 \cdot 2 \cdot 2$ .

Tap for more steps...

Step 10.1

$8$ has factors of $2$ and $4$ .

$2 \cdot 4$

Step 10.2

$4$ has factors of $2$ and $2$ .

$2 \cdot 2 \cdot 2$

Step 11

The number $1$ is not a prime number because it only has one positive factor, which is itself.

Not prime

Step 12

The prime factors for $8$ are $2 \cdot 2 \cdot 2$ .

Tap for more steps...

Step 12.1

$8$ has factors of $2$ and $4$ .

$2 \cdot 4$

Step 12.2

$4$ has factors of $2$ and $2$ .

$2 \cdot 2 \cdot 2$

Step 13

Since $13$ has no factors besides $1$ and $13$ .

$13$ is a prime number

Step 14

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

$3 \cdot 5$

Step 15

The prime factors for $24$ are $2 \cdot 2 \cdot 2 \cdot 3$ .

Tap for more steps...

Step 15.1

$24$ has factors of $2$ and $12$ .

$2 \cdot 12$

Step 15.2

$12$ has factors of $2$ and $6$ .

$2 \cdot 2 \cdot 6$

Step 15.3

$6$ has factors of $2$ and $3$ .

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

Step 16

Since $17$ has no factors besides $1$ and $17$ .

$17$ is a prime number

Step 17

Since $13$ has no factors besides $1$ and $13$ .

$13$ is a prime number

Step 18

$4$ has factors of $2$ and $2$ .

$2 \cdot 2$

Step 19

$10$ has factors of $2$ and $5$ .

$2 \cdot 5$

Step 20

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

$3 \cdot 5$

Step 21

The prime factors for $20$ are $2 \cdot 2 \cdot 5$ .

Tap for more steps...

Step 21.1

$20$ has factors of $2$ and $10$ .

$2 \cdot 10$

Step 21.2

$10$ has factors of $2$ and $5$ .

$2 \cdot 2 \cdot 5$

Step 22

The LCM of $3, 7, 13, 19, 22, 21, 17, 10, 8, 1, 8, 13, 15, 24, 17, 13, 4, 10, 15, 20$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$

Step 23

Multiply $2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$ .

Tap for more steps...

Step 23.1

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$

Step 23.2

Multiply $4$ by $2$ .

$8 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$

Step 23.3

Multiply $8$ by $3$ .

$24 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$

Step 23.4

Multiply $24$ by $5$ .

$120 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19$

Step 23.5

Multiply $120$ by $7$ .

$840 \cdot 11 \cdot 13 \cdot 17 \cdot 19$

Step 23.6

Multiply $840$ by $11$ .

$9240 \cdot 13 \cdot 17 \cdot 19$

Step 23.7

Multiply $9240$ by $13$ .

$120120 \cdot 17 \cdot 19$

Step 23.8

Multiply $120120$ by $17$ .

$2042040 \cdot 19$

Step 23.9

Multiply $2042040$ by $19$ .

$38798760$