Finite Math Examples

1

$1$ ,

4

$4$ ,

7

$7$ ,

10

$10$

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 number

1

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

Not prime

Step 3

4

$4$ has factors of

2

$2$ and

2

$2$ .

2 \cdot 2

$2 \cdot 2$

Step 4

Since

7

$7$ has no factors besides

1

$1$ and

7

$7$ .

7

$7$ is a prime number

Step 5

10

$10$ has factors of

2

$2$ and

5

$5$ .

2 \cdot 5

$2 \cdot 5$

Step 6

The LCM of

1, 4, 7, 10

$1, 4, 7, 10$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

2 \cdot 2 \cdot 5 \cdot 7

$2 \cdot 2 \cdot 5 \cdot 7$

Step 7

Multiply

2 \cdot 2 \cdot 5 \cdot 7

$2 \cdot 2 \cdot 5 \cdot 7$ .

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Step 7.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 5 \cdot 7

$4 \cdot 5 \cdot 7$

Step 7.2

Multiply

4

$4$ by

5

$5$ .

20 \cdot 7

$20 \cdot 7$

Step 7.3

Multiply

20

$20$ by

7

$7$ .

140

$140$

140

$140$