## Monday, October 06, 2014

### Help With GED Math Problems: Finding Lowest Common Denominator for Fractions

Building the LCD or lowest common denominators for two or more fractions can be challenging.  But it is an important skill for knowing how to add and subtract fractions and one that anyone studying their GED math test will need to know.

First step:  Take each denominator and factor to product of prime numbers.
Second step:  Build the lowest common denominator by using each factor with the greatest exponent.

What is the lowest common denominator for the following fractions: 7/12, 7/15, 19/30?  Use the product of prime factor method.

12 = 2 x 2 x 3 or 2^2 x 3
15 = 3 x 5
30 = 2 x 3 x 5

Build the lowest common denominator by using each factor (i.e. 2^2) with the greatest exponents.

If I were demonstrating the concept of building lowest common denominators to students, it would go something like this, " Let's start with the denominator twelve.  The denominator 12 needs at least two twos and a three.  The denominator fifteen needs a three, but because we have one from the twelve... we do not need to write another one.  However, the denominator twelve needs a five, so we need to add a five.  The denominator thirty needs a two... which we have so we do not need to add one. It also needs a three and a five, but because we already have both, again we do not need to add.  We have now build our LCD and all we need to do is multiply the factors together. So 2 x 2 x 3 x 5 = 60.  The LCD of 12, 15, and 30 is 60.

LCD = 2 x 2 x 3 x 5 = 60