GCF + LCM with Variables

When working with variable expressions, such as 40a3b, we treat the variables as prime factors.

We know that 4a is a factor of 40a3b and 40a3b is a multiple of 4a because the prime factorization of 4a is inside of the prime factorization of 40a3b.

On the other hand, 10ab2 is not a factor of 40a3b and 40a3b is not a multiple of 10ab2 because the prime factorization of 10ab2 is not inside of the prime factorization of 40a3b.

Finding All Common Factors

Find all of the common factors of:

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Use the keypad to enter the prime factorizations of each common factor.

Finding the Greatest Common Factor (GCF)

Find the greatest common factor of and .

Use the keypad to add prime factors to the prime factorization of a common factor. When it is no longer possible to add any more prime factors, the common factor is the greatest common factor.

Identifying Common Multiples

Tap on the common multiples of:

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Finding the Least Common Multiple (LCM)

Find the least common multiple of and .

Use the keypad to add enough prime factors to fit prime factorizations. If prime factorizations fit with no extra prime factors, the common multiple is the least common multiple.

Using Exponents to Find the GCF or LCM

of and .