# LCM and GCF of 10 and 25 using prime factorization

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 2 and 4 would be 2.
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 10 and 25 equals 5

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 10 and 25 equals 50

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
10 and 25 = 5

The Least Common Multiple, Least Common Denominator, Least Common Divisor of
10 and 25 = 50

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