The GCF or greatest common factor is the largest positive integer that will divide into each number evenly.

For example, the greatest common factor of 9 and 12 would be 15.

There are several different names for the GCF ( greatest common factor)

- GCD Greatest Common Denominator
- HCF Highest Common Factor
- GCD Greatest Common Divisor

**The GCF for 9, 12 and 15 equals 3**

The lcm or least common multiple is the smallest positive integer that two or more numbers will divide into evenly. Again, a zero remainder.

Other names for the LCM

- LCD Least Common Denominator
- LCD Least Common Divisor

**The LCM of 9,12 and 15 = 180**

I like to use a factor tree to find the LCM and the GCF

Once you find all of the prime factors of a number, to find the GCF you multiply all of the factors, but multiply duplicates in each number only once.

In order to calculate the LCM you look for factors in each number and multiply these common positive integers together.

In summary,

The Greatest Common Factor, Greatest Common Denominator, Highest Common Factor of

**9,12, and 15 = 3**

The Least Common Multiple, Least Common Denominator, Least Common Divisor of

**9,12, and 15 = 180**

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