Find the LCM 28 , 98 , 154

$28$ , $98$ , $154$

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 $28$ are $2 \cdot 2 \cdot 7$ .

$28$ has factors of $2$ and $14$ .

$2 \cdot 14$

$14$ has factors of $2$ and $7$ .

$2 \cdot 2 \cdot 7$

Step 3

The prime factors for $98$ are $2 \cdot 7 \cdot 7$ .

$98$ has factors of $2$ and $49$ .

$2 \cdot 49$

$49$ has factors of $7$ and $7$ .

$2 \cdot 7 \cdot 7$

Step 4

The prime factors for $154$ are $2 \cdot 7 \cdot 11$ .

$154$ has factors of $2$ and $77$ .

$2 \cdot 77$

$77$ has factors of $7$ and $11$ .

$2 \cdot 7 \cdot 11$

Step 5

The LCM of $28, 98, 154$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

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

Step 6

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

Multiply $2$ by $2$ .

$4 \cdot 7 \cdot 7 \cdot 11$

Multiply $4$ by $7$ .

$28 \cdot 7 \cdot 11$

Multiply $28$ by $7$ .

$196 \cdot 11$

Multiply $196$ by $11$ .

$2156$