Basic Math Examples

84

$84$ ,

30

$30$

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

84

$84$ are

2 \cdot 2 \cdot 3 \cdot 7

$2 \cdot 2 \cdot 3 \cdot 7$ .

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Step 2.1

84

$84$ has factors of

2

$2$ and

42

$42$ .

2 \cdot 42

$2 \cdot 42$

Step 2.2

42

$42$ has factors of

2

$2$ and

21

$21$ .

2 \cdot 2 \cdot 21

$2 \cdot 2 \cdot 21$

Step 2.3

21

$21$ has factors of

3

$3$ and

7

$7$ .

2 \cdot 2 \cdot 3 \cdot 7

$2 \cdot 2 \cdot 3 \cdot 7$

2 \cdot 2 \cdot 3 \cdot 7

$2 \cdot 2 \cdot 3 \cdot 7$

Step 3

The prime factors for

30

$30$ are

2 \cdot 3 \cdot 5

$2 \cdot 3 \cdot 5$ .

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Step 3.1

30

$30$ has factors of

2

$2$ and

15

$15$ .

2 \cdot 15

$2 \cdot 15$

Step 3.2

15

$15$ has factors of

3

$3$ and

5

$5$ .

2 \cdot 3 \cdot 5

$2 \cdot 3 \cdot 5$

2 \cdot 3 \cdot 5

$2 \cdot 3 \cdot 5$

Step 4

The LCM of

84, 30

$84, 30$ 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 \cdot 7

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 7$

Step 5

Multiply

2 \cdot 2 \cdot 3 \cdot 5 \cdot 7

$2 \cdot 2 \cdot 3 \cdot 5 \cdot 7$ .

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 3 \cdot 5 \cdot 7

$4 \cdot 3 \cdot 5 \cdot 7$

Step 5.2

Multiply

4

$4$ by

3

$3$ .

12 \cdot 5 \cdot 7

$12 \cdot 5 \cdot 7$

Step 5.3

Multiply

12

$12$ by

5

$5$ .

60 \cdot 7

$60 \cdot 7$

Step 5.4

Multiply

60

$60$ by

7

$7$ .

420

$420$

420

$420$