Algebra Examples

72

$72$

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

72

$72$ are

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

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

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Step 2.1

72

$72$ has factors of

2

$2$ and

36

$36$ .

2 \cdot 36

$2 \cdot 36$

Step 2.2

36

$36$ has factors of

2

$2$ and

18

$18$ .

2 \cdot 2 \cdot 18

$2 \cdot 2 \cdot 18$

Step 2.3

18

$18$ has factors of

2

$2$ and

9

$9$ .

2 \cdot 2 \cdot 2 \cdot 9

$2 \cdot 2 \cdot 2 \cdot 9$

Step 2.4

9

$9$ has factors of

3

$3$ and

3

$3$ .

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

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

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

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

Step 3

Multiply

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

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

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Step 3.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 2 \cdot 3 \cdot 3

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

Step 3.2

Multiply

4

$4$ by

2

$2$ .

8 \cdot 3 \cdot 3

$8 \cdot 3 \cdot 3$

Step 3.3

Multiply

8

$8$ by

3

$3$ .

24 \cdot 3

$24 \cdot 3$

Step 3.4

Multiply

24

$24$ by

3

$3$ .

72

$72$

72

$72$

72

$72$

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