Find the greatest common factor and least common multiple of two or more whole numbers with this free GCF and LCM calculator.
Step 1:
Find the prime factorization of each number.
Step 2:
For GCF, keep only the prime factors shared by all numbers, using the smallest exponent.
Step 3:
For LCM, include every prime factor that appears, using the largest exponent.
Two-number method:
LCM(a,b) = |a×b| ÷ GCF(a,b)
GCF helps simplify fractions, reduce ratios, and group items evenly. LCM helps match repeating cycles, add fractions, and solve scheduling problems.
They are used in arithmetic, algebra, number theory, measurement, and everyday math.
Your result shows the greatest common factor and least common multiple for the numbers entered. It also shows prime factorizations and how the common or needed factors build each answer.
This makes it easier to check your work and see why the GCF and LCM are different.
GCF stands for greatest common factor, the largest factor shared by all the numbers.
LCM stands for least common multiple, the smallest multiple shared by all the numbers.
GCF looks at shared factors, while LCM looks at shared multiples.
Yes. That happens when the numbers are the same or when one number set leads to the same shared factor and multiple.