Question 1

What is the Greatest Common Factor (GCF)?

Accepted Answer

The GCF (also called GCD - Greatest Common Divisor) is the largest number that divides evenly into two or more numbers. For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without a remainder.

Question 2

What is the Least Common Multiple (LCM)?

Accepted Answer

The LCM is the smallest positive number that is a multiple of two or more numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.

Question 3

How do I find the GCF using prime factorization?

Accepted Answer

To find the GCF by prime factorization: 1) Find the prime factors of each number. 2) Identify all common prime factors. 3) Multiply the common factors (using the lowest power). For 12=2²×3 and 18=2×3², the common factors are 2 and 3, so GCF=2×3=6.

Question 4

How do I find the LCM using prime factorization?

Accepted Answer

To find the LCM by prime factorization: 1) Find the prime factors of each number. 2) Take each prime factor to its highest power. 3) Multiply them all together. For 12=2²×3 and 18=2×3², LCM=2²×3²=36.

Question 5

What is the Euclidean algorithm for GCF?

Accepted Answer

The Euclidean algorithm repeatedly divides the larger number by the smaller and replaces the larger with the remainder until the remainder is 0. For GCF(48, 18): 48÷18=2 remainder 12, then 18÷12=1 remainder 6, then 12÷6=2 remainder 0. The last non-zero remainder (6) is the GCF.

Question 6

How are GCF and LCM related?

Accepted Answer

For two numbers a and b: GCF(a,b) × LCM(a,b) = a × b. This means if you know the GCF, you can find the LCM: LCM = (a × b) / GCF. For 12 and 18: GCF=6, LCM=(12×18)/6=216/6=36.

Question 7

Can I find GCF and LCM of more than two numbers?

Accepted Answer

Yes! For GCF of multiple numbers, find the GCF of the first two, then find the GCF of that result with the next number, and repeat. For LCM, do the same but with LCM operations. This calculator supports any number of inputs.

Question 8

Where are GCF and LCM used in real life?

Accepted Answer

GCF is used for simplifying fractions, dividing items into equal groups, and tiling problems. LCM is used for finding when events sync up (e.g., buses arriving together), finding common denominators for adding fractions, and scheduling repeating events.

🔢 GCF & LCM Calculator

Enter Numbers

📖 How GCF & LCM Work

🔗 Related Tools