GCD and LCM Calculator

The Greatest Common Divisor (GCD) is the largest number that divides both numbers evenly. The Least Common Multiple (LCM) is the smallest positive number divisible by both. These concepts are fundamental in simplifying fractions and number theory.

1. 1

   Enter First Number

   Input the first positive integer

2. 2

   Enter Second Number

   Input the second positive integer

3. 3

   Calculate GCD

   The calculator uses the Euclidean algorithm to find GCD

4. 4

   Calculate LCM

   LCM is computed using: LCM = |a x b| / GCD

• 1

  GCD is always less than or equal to the smaller number

• 2

  LCM is always greater than or equal to the larger number

• 3

  GCD(a,b) x LCM(a,b) = |a x b|

• 4

  If GCD = 1, the numbers are coprime (relatively prime)

• Confusing GCD and LCM - GCD divides the numbers, numbers divide LCM

• Using GCD/LCM with negative numbers - always use absolute values

• Assuming LCM = a x b always - this is only true when GCD = 1

• Forgetting that GCD(a, 0) = a