Is the LCM (least common multiple) the same as the LCD (least common domnitator?

Question

Is the LCM (least common multiple) the same as the LCD (least common domnitator

Answer 1

Yes, In arithmetic and number theory the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. If there is no such positive integer, e.g., if a = 0 or b = 0, then lcm(a, b) is defined to be zero.



The least common denominator/multiple of two or more non-zero denominators is actually the smallest whole number that is divisible by each of the denominators

Example: Suppose we wanted to add 1/5 + 1/6 + 1/15. We would find the least common denominator as follows...

First we list the multiples of each denominator.

Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...

Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...

Multiples of 15 are 30, 45, 60, 75, 90,....

Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.

Answer 2

In reality, they are not the same thing. Make sure to look at the definitions I put here. Always be care when using these terms because sometimes they cannot be interchangable.


In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of vulgar fractions.

It is the smallest (non-zero) number that is a multiple of the denominators. For instance, the LCD of {1/2, 1/4} is 4 because the least common multiple of 2 and 4 is 4. Likewise the LCD of {1/2, 1/3} is 6.

By using this (or any multiple of it) as a denominator, it enables addition, subtraction or comparison of fractions:

1/2 + 1/4 = 2/4 + 1/4 = 3/4;
1/2 − 1/3 = 3/6 − 2/6 = 1/6;
1/3 < 2/5 since 5/15 < 6/15.

In arithmetic and number theory the LEAST COMMON MULTIPLE or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. If there is no such positive integer, e.g., if a = 0 or b = 0, then lcm(a, b) is defined to be zero.

Answer 3

Yeah, except that the LCD is for denominators only, but the LCM is for all integers.