Basic Math Examples

65

$65$ ,

78

$78$

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

65

$65$ has factors of

5

$5$ and

13

$13$ .

5 \cdot 13

$5 \cdot 13$

Step 3

The prime factors for

78

$78$ are

2 \cdot 3 \cdot 13

$2 \cdot 3 \cdot 13$ .

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Step 3.1

78

$78$ has factors of

2

$2$ and

39

$39$ .

2 \cdot 39

$2 \cdot 39$

Step 3.2

39

$39$ has factors of

3

$3$ and

13

$13$ .

2 \cdot 3 \cdot 13

$2 \cdot 3 \cdot 13$

2 \cdot 3 \cdot 13

$2 \cdot 3 \cdot 13$

Step 4

The LCM of

65, 78

$65, 78$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

2 \cdot 3 \cdot 5 \cdot 13

$2 \cdot 3 \cdot 5 \cdot 13$

Step 5

Multiply

2 \cdot 3 \cdot 5 \cdot 13

$2 \cdot 3 \cdot 5 \cdot 13$ .

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Step 5.1

Multiply

2

$2$ by

3

$3$ .

6 \cdot 5 \cdot 13

$6 \cdot 5 \cdot 13$

Step 5.2

Multiply

6

$6$ by

5

$5$ .

30 \cdot 13

$30 \cdot 13$

Step 5.3

Multiply

30

$30$ by

13

$13$ .

390

$390$

390

$390$