# Math Fractions Help: GCF and LCM

Jun 1st 2020

## Fractions, in a glance

Fraction has two parts: the numerator or the top number indicating how many parts you have; and the denominator or the bottom number which tells how many parts the whole is divided into. Proper fraction is when the number in the numerator is less than the denominator while improper fraction is where the numerator is greater than the denominator. Mixed number is a combination of a whole number and a fraction while the concept of reciprocal means the denominator becomes the numerator while the numerator becomes the denominator.

## Greatest Common Factor (GCF)

The greatest common factor is the largest number that can evenly divide two or more numbers. This is particularly important when simplifying fractions. In finding the CGF, the following should be done: Consider the numbers 18 and 24 to better understand this topic.

1) List all the prime factors of each factor, usually odd numbers. Prime Factors of 18: 2 x 3 x 3 Prime Factors of 24: 2 x 2 x 2 x3

2) Determine the common factors which are present in both numbers. Multiply the prime factors. If there are no prime factors for each number, then the GCF should be 1.

In the given example, 2 and 3 are the common prime factors. Multiply 2 by 3 which will you give you a product of 6. Hence, GCF is 6.

## Least Common Multiple (LCM)

The least common multiple is the smallest number, aside from zero, that is a multiple of both numbers. Consider the numbers 3 and 4. Multiples of 3 consist of 0, 3, 6, 9, 12, 15, 18, 21 and 24 while that of 4 are 0, 4, 8, 12, 16, 20, 24 and 28. Common multiples aside from 0 are 12 and 24 and the LCM of both numbers is 12 being the least number between the two.

Once you master these two concepts, you surely won't need any math fractions help.