# Praxis Core Prep: How to Find the Greatest Common Factor and Least Common Multiple

Greatest common factor and least common multiple are phrases that tend the throw people when they go to take the Praxis Core. Two whole numbers can have factors in common. Such factors are called *common factors.* The greatest of those factors is the *greatest common factor* of the two numbers.

To find the greatest common factor of two numbers, find all the factors of both numbers, determine which factors the numbers have in common, and then determine which of those common factors is the greatest (largest).

For example, to determine the greatest common factor of 20 and 45, you must first determine the factors of both numbers. You can use the prime factorization technique to find them.

20 : 1, 2, 4, 5, 10, 20

45 : 1, 3, 5, 9, 15, 45

What factors do 20 and 45 have in common? The common factors are 1 and 5. Because 5 is the greatest of the common factors, 5 is the greatest common factor.

The *least common multiple* of two numbers is like the greatest common factor, except that it’s the lowest number instead of the highest one, and it’s a multiple instead of a factor. To find the least common multiple of two numbers, write out several multiples of each and then determine the lowest multiple that they have in common.

For example, to find the least common multiple of 3 and 5, first write multiples of both numbers until you see one that they have in common.

3 : 3, 6, 9, 12, 15, 18, 21

5 : 5, 10, 15

For 5, you can stop at 15 because 15 is also a multiple of 3. Because 15 is the lowest of the multiples that 3 and 5 have in common, 15 is the least common multiple of 3 and 15.

You can’t just multiply the factors together to get the least common multiple. Multiplying the factors will give you a multiple, but it may not be the smallest one. For example, if you want the least common multiple of 4 and 6, you can’t multiply them because that gives you 24, when the least common multiple is actually 12.