48 and 18
48 = 2 × 18 + 12, 18 = 1 × 12 + 6, 12 = 2 × 6 + 0, so the GCD is 6 and the LCM is 48 × 18 ÷ 6 = 144.
GCD and LCM Calculator
Find the greatest common divisor and least common multiple of two or more numbers, with Euclid's steps.
Result
Enter your values and select Calculate to see the result.
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How the GCD and LCM Calculator works
Enter two or more whole numbers. The greatest common divisor (GCD, also called HCF) is the largest number that divides all of them; the least common multiple (LCM) is the smallest number they all divide into. The GCD uses Euclid's algorithm, whose steps are shown for the first two numbers, and the LCM is exact even when it's very large.
Formulas
Euclid's algorithm
gcd(a, b) = gcd(b, a mod b), until the remainder is 0
LCM
lcm(a, b) = |a × b| ÷ gcd(a, b)
Examples
12, 18 and 30
GCD 6, LCM 180.
Frequently asked questions
What are GCD and LCM used for?
Simplifying fractions (divide by the GCD) and adding fractions (use the LCM as the common denominator).
What about negative numbers?
Signs are ignored: the GCD and LCM are always positive.
Why can't I use 0?
Every number divides 0, so the LCM isn't defined with 0.
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