Find the LCM 12 , 36 , 54 , 85 , 92 , 13

$12$ , $36$ , $54$ , $85$ , $92$ , $13$

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 $12$ are $2 \cdot 2 \cdot 3$ .

$12$ has factors of $2$ and $6$ .

$2 \cdot 6$

$6$ has factors of $2$ and $3$ .

$2 \cdot 2 \cdot 3$

Step 3

The prime factors for $36$ are $2 \cdot 2 \cdot 3 \cdot 3$ .

$36$ has factors of $2$ and $18$ .

$2 \cdot 18$

$18$ has factors of $2$ and $9$ .

$2 \cdot 2 \cdot 9$

$9$ has factors of $3$ and $3$ .

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

Step 4

The prime factors for $54$ are $2 \cdot 3 \cdot 3 \cdot 3$ .

$54$ has factors of $2$ and $27$ .

$2 \cdot 27$

$27$ has factors of $3$ and $9$ .

$2 \cdot 3 \cdot 9$

$9$ has factors of $3$ and $3$ .

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

Step 5

$85$ has factors of $5$ and $17$ .

$5 \cdot 17$

Step 6

The prime factors for $92$ are $2 \cdot 2 \cdot 23$ .

$92$ has factors of $2$ and $46$ .

$2 \cdot 46$

$46$ has factors of $2$ and $23$ .

$2 \cdot 2 \cdot 23$

Step 7

Since $13$ has no factors besides $1$ and $13$ .

$13$ is a prime number

Step 8

The LCM of $12, 36, 54, 85, 92, 13$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 23$

Step 9

Multiply $2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 23$ .

Multiply $2$ by $2$ .

$4 \cdot 3 \cdot 3 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 23$

Multiply $4$ by $3$ .

$12 \cdot 3 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 23$

Multiply $12$ by $3$ .

$36 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 23$

Multiply $36$ by $3$ .

$108 \cdot 5 \cdot 13 \cdot 17 \cdot 23$

Multiply $108$ by $5$ .

$540 \cdot 13 \cdot 17 \cdot 23$

Multiply $540$ by $13$ .

$7020 \cdot 17 \cdot 23$

Multiply $7020$ by $17$ .

$119340 \cdot 23$

Multiply $119340$ by $23$ .

$2744820$

Find the LCM 12 , 36 , 54 , 85 , 92 , 13

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