## The Difference Among LCM, LCD, GCD and GCF

**LCM and LCD**

LCM means Least Common Multiple. Multiple in this context is used for integers. LCD, on the other hand, means Least Common Denominator. As we know, denominator is used in fractions.

So, in 1/3 and 1/4, should we say, LCM or LCD?

CORRECT STATEMENT: LCM of 3 and 4 (multiple is used for integers).

CORRECT STATEMENT: LCD of 1/3 and 1/4 (denominator is used for fractions).

It is INCORRECT to say LCM of 1/3 and 1/4.

Notice that the LCM of 3 and 4 and the LCD of 1/3 and 1/4 is 12. That’s why most people use them interchangeably.

**GCF and GCD**

GCF means Greatest Common Factor

A factor of an integer is an integer that can be **multiplied** with another integer to get the given integer. For example, 3 is a factor of 6 because 3 x 2 = 6.

A divisor of an integer is an integer that **divides** that integer (without a remainder). For example, 3 is a divisor of 6 because 6/3 = 2, which is an integer.

Basically, factors and divisors have the same meaning when it comes to integers. Factor, however, is the term used in multiplication, while divisor is the term used for division. Here are some examples.

Positive factors of 12 are 1, 2, 4, 6, 12.

Positive divisors of 12 are 1, 2, 4, 6, 12.

GCF and GCD have the same meaning and will give the same values.