Angol Matematika

Greatest Common Divisor and Lowest Common Multiple

The GCD of two or more whole numbers is the largest whole number that divides each of the numbers.

The LCM of two or more whole numbers is the smallest whole number that is divisible by each of the numbers.

We list the numbers whose common divisor is to be defined between parentheses, the numbers must be separated by semi-colons. (a;b)

Calculating GCD:

1. Break the numbers down into their prime factors.

2. Find those prime factors which appear in all the groups of prime factors.

3. Find the largest possible power of the primes.

4. Multiply them.

The GCD of (relatively) primes is necessarily 1.

Calculating LCM:

5. Break the numbers down into their prime factors.<br />

6. Find those prime factors which appear in any groups of prime factors.

7. Find the largest possible power of the primes that occur.

8. Multiply them.

The LCM of two whole numbers (a;b), where a is divisible by b, is a.

The product of LCM and GCD is equal to the product of the numbers.

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