Algebra Examples

15

$15$

12

$12$

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

15

$15$ has factors of

3

$3$ and

5

$5$ .

3 \cdot 5

$3 \cdot 5$

Step 3

The prime factors for

12

$12$ are

2 \cdot 2 \cdot 3

$2 \cdot 2 \cdot 3$ .

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Step 3.1

12

$12$ has factors of

2

$2$ and

6

$6$ .

2 \cdot 6

$2 \cdot 6$

Step 3.2

6

$6$ has factors of

2

$2$ and

3

$3$ .

2 \cdot 2 \cdot 3

$2 \cdot 2 \cdot 3$

2 \cdot 2 \cdot 3

$2 \cdot 2 \cdot 3$

Step 4

The LCM of

15, 12

$15, 12$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

2 \cdot 2 \cdot 3 \cdot 5

$2 \cdot 2 \cdot 3 \cdot 5$

Step 5

Multiply

2 \cdot 2 \cdot 3 \cdot 5

$2 \cdot 2 \cdot 3 \cdot 5$ .

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 3 \cdot 5

$4 \cdot 3 \cdot 5$

Step 5.2

Multiply

4

$4$ by

3

$3$ .

12 \cdot 5

$12 \cdot 5$

Step 5.3

Multiply

12

$12$ by

5

$5$ .

60

$60$

60

$60$

15 12

$15 12$

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