GCF and LCM Worksheets with Answers

Whether you are a teacher looking for resources to help your students practice finding the greatest common factor (GCF) and least common multiple (LCM), or a student in need of extra practice, our GCF and LCM worksheets with answers are here to assist you.

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What is GCF (Greatest Common Factor)?

The Greatest Common Factor (GCF) is the largest number that divides evenly into two or more given numbers without leaving a remainder. It is the highest value that is a common factor of all the numbers being considered.

What is LCM (Least Common Multiple)?

The Least Common Multiple (LCM) is the smallest multiple that two or more numbers have in common. It is the smallest number that is evenly divisible by all the numbers being considered, without leaving a remainder._CALC.WAIT

How do you find the GCF of two numbers?

To find the greatest common factor (GCF) of two numbers, you list all the factors of each number and identify the largest factor that both numbers share. This common factor is the GCF of the two numbers. You can also use prime factorization to find the GCF by breaking down each number into its prime factors and then identifying the common prime factors along with the lowest exponent for each common prime factor.

How do you find the LCM of two numbers?

To find the least common multiple (LCM) of two numbers, you can start by listing the multiples of each number and then identifying the smallest number that is a multiple of both. Another method is to factorize each number into its prime factors and then multiply the highest power of each prime factor present in either number. This resulting product will be the LCM of the two numbers.

Can the GCF of two numbers be larger than either of the numbers?

No, the Greatest Common Factor (GCF) of two numbers cannot be larger than either of the numbers. The GCF is always a positive integer that divides both numbers without leaving a remainder, so it must be a factor of both numbers and therefore smaller than or equal to the smaller of the two numbers.

Can the LCM of two numbers be smaller than either of the numbers?

No, the least common multiple (LCM) of two numbers cannot be smaller than either of the numbers. The LCM is always equal to or greater than the largest of the two numbers being considered, as it is a multiple of both numbers.

What is the GCF of 12 and 18?

The greatest common factor (GCF) of 12 and 18 is 6.

What is the LCM of 6 and 9?

The least common multiple (LCM) of 6 and 9 is 18.

How can you use prime factorization to find the GCF and LCM?

To find the greatest common factor (GCF) using prime factorization, list the prime factors of each number and identify the common prime factors with the lowest exponents. Multiply these common prime factors together to get the GCF. For the least common multiple (LCM), list the prime factors of each number and include all unique prime factors with the highest exponents. Multiply these prime factors together to get the LCM. By using prime factorization, you can efficiently find both the GCF and LCM of numbers.

How can GCF and LCM help simplify fractions?

The greatest common factor (GCF) and least common multiple (LCM) are used to simplify fractions by finding the largest number that can evenly divide both the numerator and the denominator. By simplifying a fraction using the GCF, you can reduce the fraction to its simplest form, making it easier to work with and understand. Similarly, using the LCM can help identify a common multiple that can be used to simplify fractions by scaling both the numerator and denominator to a common value. This simplification process can make fractions easier to compare, add, subtract, or perform other mathematical operations on them.