Find the LCM LCM: 24 and 52

LCM: $24$ and $52$

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.

The prime factors for $24$ are $2 \cdot 2 \cdot 2 \cdot 3$ .

$24$ has factors of $2$ and $12$ .

$2 \cdot 12$

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

$2 \cdot 2 \cdot 6$

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

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

The prime factors for $52$ are $2 \cdot 2 \cdot 13$ .

$52$ has factors of $2$ and $26$ .

$2 \cdot 26$

$26$ has factors of $2$ and $13$ .

$2 \cdot 2 \cdot 13$

The LCM of $24, 52$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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

The LCM of $24, 52$ is $2 \cdot 2 \cdot 2 \cdot 3 \cdot 13 = 312$ .

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 3 \cdot 13$

Multiply $4$ by $2$ .

$8 \cdot 3 \cdot 13$

Multiply $8$ by $3$ .

$24 \cdot 13$

Multiply $24$ by $13$ .

$312$