Find the LCM 12 , 60

$12$ , $60$

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 $60$ are $2 \cdot 2 \cdot 3 \cdot 5$ .

$60$ has factors of $2$ and $30$ .

$2 \cdot 30$

$30$ has factors of $2$ and $15$ .

$2 \cdot 2 \cdot 15$

$15$ has factors of $3$ and $5$ .

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

Step 4

Multiply $2 \cdot 2 \cdot 3 \cdot 5$ .

Multiply $2$ by $2$ .

$4 \cdot 3 \cdot 5$

Multiply $4$ by $3$ .

$12 \cdot 5$

Multiply $12$ by $5$ .

$60$