GCF and LCM

Greatest Common Factor

       The greatest common factor (GCF) of two or more numbers is the greatest number - which divides each number exactly. GCF can be determined by the following:

       Prime factorization

• Step 1:       Express each given number as a product of its prime factors.
• Step 2:       Write all the prime factors common to all the numbers. Their product is the GCF.

       Euclid's method

• Step 1:       Divide the larger number by the smaller number.
• Step 2:       Divide the smaller number by the remainder obtained.
• Step 3:       Divide the remainder of step 1 by the remainder obtained in step 2.
• Step 4:       Continue until no remainder is left and the last divisor or the nonzero remainder is the required GCF.

Multiples

       When we multiply a number by 1, 2, 3, 4, and so on, we get multiples of that number.

       The multiples of 5 are 5, 10, 15, 20, ...

5 x 1, 5 x 2, 5 x 3, 5 x 4

       Similarly, the multiples of 7 are 7, 14, 21, 28, ...; and the multiples of 9 are 9, 18, 27, 36, ...

The multiples of a number are all those numbers which can be divided by the given number.

Common Multiples

       Common multiples of two or more numbers are the numbers which can be divided by each of the given numbers. For example:

       The multiples of 2 are 2, 4, 6, 8, 10, 12, ...

       The multiples of 3 are 3, 6, 9, 12, 15, 18, ...

       Therefore, the common multiples of 2 and 3 are 6, 12, 18, and so on.