Algebra Examples

24

$24$ ,

36

$36$ ,

60

$60$

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

24

$24$ are

2 \cdot 2 \cdot 2 \cdot 3

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

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Step 2.1

24

$24$ has factors of

2

$2$ and

12

$12$ .

2 \cdot 12

$2 \cdot 12$

Step 2.2

12

$12$ has factors of

2

$2$ and

6

$6$ .

2 \cdot 2 \cdot 6

$2 \cdot 2 \cdot 6$

Step 2.3

6

$6$ has factors of

2

$2$ and

3

$3$ .

2 \cdot 2 \cdot 2 \cdot 3

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

2 \cdot 2 \cdot 2 \cdot 3

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

Step 3

The prime factors for

36

$36$ are

2 \cdot 2 \cdot 3 \cdot 3

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

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Step 3.1

36

$36$ has factors of

2

$2$ and

18

$18$ .

2 \cdot 18

$2 \cdot 18$

Step 3.2

18

$18$ has factors of

2

$2$ and

9

$9$ .

2 \cdot 2 \cdot 9

$2 \cdot 2 \cdot 9$

Step 3.3

9

$9$ has factors of

3

$3$ and

3

$3$ .

2 \cdot 2 \cdot 3 \cdot 3

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

2 \cdot 2 \cdot 3 \cdot 3

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

Step 4

The prime factors for

60

$60$ are

2 \cdot 2 \cdot 3 \cdot 5

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

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Step 4.1

60

$60$ has factors of

2

$2$ and

30

$30$ .

2 \cdot 30

$2 \cdot 30$

Step 4.2

30

$30$ has factors of

2

$2$ and

15

$15$ .

2 \cdot 2 \cdot 15

$2 \cdot 2 \cdot 15$

Step 4.3

15

$15$ has factors of

3

$3$ and

5

$5$ .

2 \cdot 2 \cdot 3 \cdot 5

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

2 \cdot 2 \cdot 3 \cdot 5

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

Step 5

The LCM of

24, 36, 60

$24, 36, 60$ 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 3 \cdot 5

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

Step 6

Multiply

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

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

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Step 6.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 2 \cdot 3 \cdot 3 \cdot 5

$4 \cdot 2 \cdot 3 \cdot 3 \cdot 5$

Step 6.2

Multiply

4

$4$ by

2

$2$ .

8 \cdot 3 \cdot 3 \cdot 5

$8 \cdot 3 \cdot 3 \cdot 5$

Step 6.3

Multiply

8

$8$ by

3

$3$ .

24 \cdot 3 \cdot 5

$24 \cdot 3 \cdot 5$

Step 6.4

Multiply

24

$24$ by

3

$3$ .

72 \cdot 5

$72 \cdot 5$

Step 6.5

Multiply

72

$72$ by

5

$5$ .

360

$360$

360

$360$