Algebra Examples

48

$48$

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

48

$48$ are

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

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

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Step 2.1

48

$48$ has factors of

2

$2$ and

24

$24$ .

2 \cdot 24

$2 \cdot 24$

Step 2.2

24

$24$ has factors of

2

$2$ and

12

$12$ .

2 \cdot 2 \cdot 12

$2 \cdot 2 \cdot 12$

Step 2.3

12

$12$ has factors of

2

$2$ and

6

$6$ .

2 \cdot 2 \cdot 2 \cdot 6

$2 \cdot 2 \cdot 2 \cdot 6$

Step 2.4

6

$6$ has factors of

2

$2$ and

3

$3$ .

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

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

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

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

Step 3

Multiply

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

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

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Step 3.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 2 \cdot 2 \cdot 3

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

Step 3.2

Multiply

4

$4$ by

2

$2$ .

8 \cdot 2 \cdot 3

$8 \cdot 2 \cdot 3$

Step 3.3

Multiply

8

$8$ by

2

$2$ .

16 \cdot 3

$16 \cdot 3$

Step 3.4

Multiply

16

$16$ by

3

$3$ .

48

$48$

48

$48$

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