GCF and LCM

Front

What is the definition of the Greatest Common Factor (GCF)?

Back

The GCF of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

Front

What is the definition of the Least Common Multiple (LCM)?

Back

The LCM of two or more integers is the smallest positive integer that is divisible by each of the integers.

Front

How do you find the GCF of two numbers using prime factorization?

Back

1. Factor each number into its prime factors. 2. Identify the common prime factors. 3. Multiply the lowest powers of these common factors.

Front

How do you find the LCM of two numbers using prime factorization?

Back

1. Factor each number into its prime factors. 2. Identify all prime factors, taking the highest power of each. 3. Multiply these together.

Front

What is the GCF of 18 and 24?

Back

The GCF is 6.

Front

What is the LCM of 4 and 6?

Back

The LCM is 12.

Front

What is the relationship between GCF and LCM of two numbers?

Back

The product of the GCF and LCM of two numbers is equal to the product of the numbers themselves.

Front

How can you find the GCF using the Euclidean algorithm?

Back

1. Divide the larger number by the smaller number. 2. Take the remainder and divide the smaller number by this remainder. 3. Repeat until the remainder is 0; the last non-zero remainder is the GCF.

Front

What is the LCM of 15 and 25?

Back

The LCM is 75.

Front

What is the GCF of 30 and 45?

Back

The GCF is 15.