# The greatest common divisor and least common multiple

Definition: the Greatest common divisor of two or more natural numbers is called the greatest natural number that divides each of the given numbers.

For example

NOD

## Coprime numbers

Definition: Two natural numbers are called relatively Primeif their GCD is equal to one.

## Finding GCD using the decomposition into Prime factors

### To find the GCD of two or more numbers, you must:

1. To put these numbers into Prime factors.
2. To make the product of the common Prime factors taken with the smallest exponent.
3. To find the value of the work.

### The Euclidean Algorithm

1. Share on with Stacey:
2. Divide the divisor into :
3. Divide the divisor into the new balance :

The last nonzero remainder is the GCD.

## Least common multiple (LCM)

The least common multiple of two or more natural numbers is called the smallest natural number that is divisible by each of the given numbers.

HCK

For example

NSK

## The connection between the NODE and the NOC of the two numbers

NOD

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