## Monday, 4 June 2012

### Least Common Denominator

In today's session we are going to discuss about Least Common Denominator, By Least Common Denominator, we mean the LCM of the denominators of given fractions. Before we learn about Least Common Denominator, let us quickly recall the terms LCM, fractions & denominator; we are already familiar with. By LCM, we mean lowest common denominator. It can be calculated for 2 or more numbers by long division, listing of multiples of the given numbers or in the best way, by prime factorization. Now, fractions are numbers in the form a/b . A fraction, as we can see in the expression, has two parts, a & b. Here, a is the numerator & b is the denominator of the fraction. Thus, we have recalled denominator also that it is the lower part in the fraction.
Now coming back to the topic of discussion, i.e. , Least Common Denominator or LCD ; as stated above is the LCM of the denominators of two or more fractions . But why do we need to find such LCD. As we know that the fractions may be like or unlike depending on whether their denominator is same or not & also that to add or subtract fractions; the fractions must be like fractions. If the fractions to be added or subtracted are like, we can add or subtract them easily. But for unlike fractions, we need to make them like by changing their denominators to Least Common Denominator. This is done by finding the LCM of the denominators of all unlike fractions. As for example; if we have to add 3/7+2/5+4/3. Here the fractions are unlike. So we’ll find the LCM of their denominators which comes out 105. Now we can change the fractions & make their denominator 105 by finding equivalent fractions. Thus, finally we have 3/7+2/5+4/3 = (45+42+140)/105=227/105. You can find the Independent Variable Definition at different places online . Also look for ICSE class 10 syllabus online and in next session we will discuss about