When we have a set of two or more numbers, we can look for various things that these two values have in common. The greatest common factor (GCF) is a measure that defines the factor that both values share the is the largest factor possible. There two common methods that you can use to find the GCF for two values. The first method is to just list all the possible factors for each value and find where there is overlap, the highest factor that each share is the GCF. When we have large values, it is helpful to use prime factorization. This process starts by listing all factors that are primes and then multiply all the primes that they have in common together. Two values can also share a common multiple. An attribute we often use to common two numbers is there least common multiple (LCM). This is the smallest possible positive number that is a multiple of both values. The common method to solve for the LCM is to list all the multiples for both values and look for overlap. The smallest multiple that is listed is the LCM.

Students are given two integers and asked to find both the least common multiple and the greatest common factor. The least common multiple is the smallest numbers that is a multiple of both of them. This is mostly an activity to prepare us for fractions and to simplify them. The greatest common factor is a value that both digits share as the biggest factor that both integers share. The best way to approach this is to find all the factors of what you are given. Then just choose the factor that is the largest between them. These worksheets explain how to find the greatest common factors and least common multiples of numbers. Your students will practice determining least common multiples, the smallest number that is a multiple of given numbers, and greatest common factors, the largest numbers that divide two or more given numbers.