Find the LCM 160 , 4900 , 1050

$160$ , $4900$ , $1050$

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 $160$ are $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$ .

$160$ has factors of $2$ and $80$ .

$2 \cdot 80$

$80$ has factors of $2$ and $40$ .

$2 \cdot 2 \cdot 40$

$40$ has factors of $2$ and $20$ .

$2 \cdot 2 \cdot 2 \cdot 20$

$20$ has factors of $2$ and $10$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 10$

$10$ has factors of $2$ and $5$ .

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

Step 3

The prime factors for $4900$ are $2 \cdot 2 \cdot 5 \cdot 5 \cdot 7 \cdot 7$ .

$4900$ has factors of $2$ and $2450$ .

$2 \cdot 2450$

$2450$ has factors of $2$ and $1225$ .

$2 \cdot 2 \cdot 1225$

$1225$ has factors of $5$ and $245$ .

$2 \cdot 2 \cdot 5 \cdot 245$

$245$ has factors of $5$ and $49$ .

$2 \cdot 2 \cdot 5 \cdot 5 \cdot 49$

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

$2 \cdot 2 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Step 4

The prime factors for $1050$ are $2 \cdot 3 \cdot 5 \cdot 5 \cdot 7$ .

$1050$ has factors of $2$ and $525$ .

$2 \cdot 525$

$525$ has factors of $3$ and $175$ .

$2 \cdot 3 \cdot 175$

$175$ has factors of $5$ and $35$ .

$2 \cdot 3 \cdot 5 \cdot 35$

$35$ has factors of $5$ and $7$ .

$2 \cdot 3 \cdot 5 \cdot 5 \cdot 7$

Step 5

The LCM of $160, 4900, 1050$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Step 6

Multiply $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7$ .

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Multiply $4$ by $2$ .

$8 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Multiply $8$ by $2$ .

$16 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Multiply $16$ by $2$ .

$32 \cdot 3 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Multiply $32$ by $3$ .

$96 \cdot 5 \cdot 5 \cdot 7 \cdot 7$

Multiply $96$ by $5$ .

$480 \cdot 5 \cdot 7 \cdot 7$

Multiply $480$ by $5$ .

$2400 \cdot 7 \cdot 7$

Multiply $2400$ by $7$ .

$16800 \cdot 7$

Multiply $16800$ by $7$ .

$117600$

Find the LCM 160 , 4900 , 1050

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