Finite Math Examples

$(60000)$ , $(72500)$

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 $60000$ are $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5$ .

Tap for more steps...

Step 2.1

$60000$ has factors of $2$ and $30000$ .

$2 \cdot 30000$

Step 2.2

$30000$ has factors of $2$ and $15000$ .

$2 \cdot 2 \cdot 15000$

Step 2.3

$15000$ has factors of $2$ and $7500$ .

$2 \cdot 2 \cdot 2 \cdot 7500$

Step 2.4

$7500$ has factors of $2$ and $3750$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 3750$

Step 2.5

$3750$ has factors of $2$ and $1875$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 1875$

Step 2.6

$1875$ has factors of $3$ and $625$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 625$

Step 2.7

$625$ has factors of $5$ and $125$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 125$

Step 2.8

$125$ has factors of $5$ and $25$ .

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 25$

Step 2.9

$25$ has factors of $5$ and $5$ .

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

Step 3

The prime factors for $72500$ are $2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$ .

Tap for more steps...

Step 3.1

$72500$ has factors of $2$ and $36250$ .

$2 \cdot 36250$

Step 3.2

$36250$ has factors of $2$ and $18125$ .

$2 \cdot 2 \cdot 18125$

Step 3.3

$18125$ has factors of $5$ and $3625$ .

$2 \cdot 2 \cdot 5 \cdot 3625$

Step 3.4

$3625$ has factors of $5$ and $725$ .

$2 \cdot 2 \cdot 5 \cdot 5 \cdot 725$

Step 3.5

$725$ has factors of $5$ and $145$ .

$2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 145$

Step 3.6

$145$ has factors of $5$ and $29$ .

$2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 4

The LCM of $60000, 72500$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5

Multiply $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$ .

Tap for more steps...

Step 5.1

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5.2

Multiply $4$ by $2$ .

$8 \cdot 2 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5.3

Multiply $8$ by $2$ .

$16 \cdot 2 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5.4

Multiply $16$ by $2$ .

$32 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5.5

Multiply $32$ by $3$ .

$96 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5.6

Multiply $96$ by $5$ .

$480 \cdot 5 \cdot 5 \cdot 5 \cdot 29$

Step 5.7

Multiply $480$ by $5$ .

$2400 \cdot 5 \cdot 5 \cdot 29$

Step 5.8

Multiply $2400$ by $5$ .

$12000 \cdot 5 \cdot 29$

Step 5.9

Multiply $12000$ by $5$ .

$60000 \cdot 29$

Step 5.10

Multiply $60000$ by $29$ .

$1740000$