What is the relationship between LCD and LCM?

Question

Nova Allen · Accepted Answer

Lowest common denominator is the lowest common multiple of the fractions' denominators.

Lowest common denominator is the lowest number to which all the fractions can be expanded, so it is the lowest common multiple of all denominators.

Example:

Let's check the following fractions:

#1/2#,#2/3#,#5/6#.

To find the lowest common denominator of the fractions we haveto find the lowest common multoiple of the fractions' denominators:

#lcd(1/2,2/3,5/6)=lcm(2,3,6)#

To calculate the #lcm# we have to find the lowest number which can be obtained by multiplying those numbers. This number is #6# because we can multiply #2*3# and #3*2# to get #6#

Levi Adams · Answer

undefined The relationship between LCD (Least Common Denominator) and LCM (Least Common Multiple) is that the LCD is specifically used in the context of fractions, while the LCM is more generally used for finding the least common multiple of integers.

The LCD of a set of fractions is the least common multiple of the denominators of those fractions. It is used to find a common denominator when adding or subtracting fractions.

The LCM of a set of integers is the smallest positive integer that is divisible by each of the integers in the set without leaving a remainder. It is used to find a common multiple of integers.

In summary, while both LCD and LCM involve finding common multiples, the LCD is specifically tailored for fractions, whereas the LCM is used for integers.