Find the LCM 132 , 504

$132$ , $504$

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 $132$ are $2 \cdot 2 \cdot 3 \cdot 11$ .

$132$ has factors of $2$ and $66$ .

$2 \cdot 66$

$66$ has factors of $2$ and $33$ .

$2 \cdot 2 \cdot 33$

$33$ has factors of $3$ and $11$ .

$2 \cdot 2 \cdot 3 \cdot 11$

Step 3

The prime factors for $504$ are $2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7$ .

$504$ has factors of $2$ and $252$ .

$2 \cdot 252$

$252$ has factors of $2$ and $126$ .

$2 \cdot 2 \cdot 126$

$126$ has factors of $2$ and $63$ .

$2 \cdot 2 \cdot 2 \cdot 63$

$63$ has factors of $3$ and $21$ .

$2 \cdot 2 \cdot 2 \cdot 3 \cdot 21$

$21$ has factors of $3$ and $7$ .

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

Step 4

The LCM of $132, 504$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 \cdot 11$

Step 5

Multiply $2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 \cdot 11$ .

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 3 \cdot 3 \cdot 7 \cdot 11$

Multiply $4$ by $2$ .

$8 \cdot 3 \cdot 3 \cdot 7 \cdot 11$

Multiply $8$ by $3$ .

$24 \cdot 3 \cdot 7 \cdot 11$

Multiply $24$ by $3$ .

$72 \cdot 7 \cdot 11$

Multiply $72$ by $7$ .

$504 \cdot 11$

Multiply $504$ by $11$ .

$5544$