Question

What is the relationship between LCD and LCM?

Answer 1

Hint: To obtain the relation between LCD and LCM we have to know their definition first. Firstly as we know LCM is the lowest common multiple of the number which is divided by all the numbers completely. LCD is the lowest common denominator of a fraction number where we find the LCM of the denominator of a fraction value.

Complete step by step solution:
Firstly we will state the definition of the two terms given.
LCM is also known as lowest common multiple which is the lowest value which can be divided by each number completely.
LCD is the lowest common denominator of a fraction number in which we find the LCM of the denominator value which is generally used to know the highest and lowest among the given fraction by making their denominator the same.
To find the LCD of a fraction value we need to find the LCM of the denominator.
So let us take some fraction value as given below:
${\displaystyle \frac{1}{3}},{\displaystyle \frac{2}{5}},{\displaystyle \frac{7}{15}}$
So we can write the relation between LCM and LCD as below:
$lcd({\displaystyle \frac{1}{3}},{\displaystyle \frac{2}{5}},{\displaystyle \frac{7}{15}})=lcm(3,5,15)$
For getting the LCM we can see that the lowest value which is divided by all their denominators is 15.
So the LCD of the fraction given is 15.

Note: LCM is generally used in solving questions with fraction values where we make the denominator the same so that we can add or subtract the numerator depending on the operation given. The LCM of the denominator that we find to do so is known as LCD.