dopecalc

LCM Calculator

Find the Least Common Multiple (LCM) of two or more numbers using the GCD-based method. Also shows the Greatest Common Divisor (GCD).

Enter two or more positive integers, separated by commas.

About this Calculator

Find the Least Common Multiple (LCM) of two or more numbers using the GCD-based method. Also shows the Greatest Common Divisor (GCD).

Formula & Calculations

Formula

LCM(a,b) = |a*b| / GCD(a,b)
Where:
  • LCM=The smallest positive integer that is a multiple of all input numbers
  • GCD=The largest positive integer that divides all input numbers without a remainder
  • a, b, c, ...=Two or more positive integers

Assumptions

  • All input numbers must be positive integers.
  • LCM is computed pairwise using the relationship LCM(a,b) = |a*b| / GCD(a,b).
  • The result may be very large for large inputs.

Calculation Examples

Example 1

Inputs:12, 18, 30
Result:LCM = 180, GCD = 6

LCM(12,18) = 36, LCM(36,30) = 180. GCD(12,18) = 6, GCD(6,30) = 6.

Example 2

Inputs:8, 20
Result:LCM = 40, GCD = 4

LCM = |8*20| / GCD(8,20) = 160 / 4 = 40.

Frequently Asked Questions

What is the difference between GCD and LCM?

GCD is the largest number that divides all inputs evenly. LCM is the smallest number that all inputs divide into evenly. They are related by: LCM(a,b) × GCD(a,b) = |a × b|.

Can I compute LCM of more than two numbers?

Yes. LCM is associative: LCM(a,b,c) = LCM(LCM(a,b), c). The calculator applies the formula pairwise for any number of inputs.