Output

GCFLCM.C

How to Use

- This can accept two or three inputs. The last one is optional.
- Please input your integer from the left, in this order:
`i-1`

►`i-2`

►`i-3`

^{(optional)}. - Type the integer on each input.
**Minimum**value of**1**.

The**maximum**value:- For 2 inputs:
`i-1`

and`i-2`

can accept (up to)**10,000**. - For 3 inputs: each input accepts maximum value of
**500**.

- For 2 inputs:
- Hit "reset" to reset all.

Purpose

This tool can be used to teach kids about finding the GCF and LCM.

Or maybe as a reminder if you forgot the method.

Or maybe as a reminder if you forgot the method.

Example

We wanna find the GCF and LCM from

First, get the Prime factorization from both.

We can use that tree factoring method, which yields:

**4**and**14**.First, get the Prime factorization from both.

We can use that tree factoring method, which yields:

- 4 = 2 × 2 (or 2
^{2}) - 14 = 2 × 7

**GCF**

GCF is about the

Or, the largest shared common factors which can be used to divide each of the numbers without resulting remainders.

Thus, as you can see, they have the common factors of 2.

The 2 and 2

Take the one with the

That's the

If we divide 4 or 14 by 2, each division

But if we use the 2

__least exponent__of the same factors.Or, the largest shared common factors which can be used to divide each of the numbers without resulting remainders.

Thus, as you can see, they have the common factors of 2.

The 2 and 2

^{2}.Take the one with the

__least exponent__.That's the

__GCF__,**2**.If we divide 4 or 14 by 2, each division

__won't produce remainders__.But if we use the 2

^{2}or 7 as the divisor, one of the divisions will result remainders.**LCM**

LCM is about the

Or, the least positive integer which can be divided by all input numbers.

Take a look again, they share the common factors of 2 and one difference, 7.

For the

For the

Then the

In another words:

__highest exponent__of the same factors multiplied by the__different factor(s)__.Or, the least positive integer which can be divided by all input numbers.

Take a look again, they share the common factors of 2 and one difference, 7.

For the

__same factors__, take the one with the__largest exponent__, that is**2**.^{2}For the

__difference__, just take that into the multiplication.Then the

__LCM__is**2**=^{2}× 7**4 × 7**=**28**.In another words:

- The multiples of 4 = 4, 8, 12, 16, 20, 24,
**28**, 32, ... - The multiples of 14 = 14,
**28**, 42, ...

**28**is the least common multiple of 4 and 14.No common Prime factor?

Then the GCF will be

**1**, and the LCM will (still) be the method above.For example,

**3**and**5**.- The GCF is
**1**. - The LCM is
**15**(3 × 5).

—The multiplication of different factors.

Why is this important?

Well, it's not.

But in "real life", either GCF or LCM or both is/are used unconsciously in many fields of engineering.

Comparable to pattern recognition, or something else. Or not entirely.

JavaScript Library

This tool is using Math Operations for the GCF and LCM methods (and adding comma to large integer).

The Prime factorization method is from

The Prime factorization method is from

**Prime Factorization-er**tool below.