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Least Common Multiple Calculator

Find the least common multiple (LCM) of two or more integers: the smallest positive number that all of them divide into evenly. Useful for adding fractions and solving scheduling problems.

Separate numbers with commas or spaces.

Least common multiple

60

Greatest common factor
1
Numbers
4, 6, 15

How to use this calculator

  1. Enter two or more whole numbers separated by commas or spaces.
  2. The LCM is calculated exactly, even for very large results.

Formula

The LCM is computed from the GCF, which avoids listing multiples. For more than two numbers, apply it pairwise.

lcm(a, b) = |a × b| / gcd(a, b)
lcm(a, b, c) = lcm(lcm(a, b), c)

Example

  1. lcm(4, 6) = 24 / gcd(4, 6) = 24 / 2 = 12.
  2. lcm(12, 15) = 180 / 3 = 60, so lcm(4, 6, 15) = 60.

Frequently asked questions

What is the least common denominator?

The least common denominator of several fractions is the LCM of their denominators. For 1/4 + 1/6, the LCD is 12.

What is the LCM of a number and 0?

By convention it is 0, since 0 is a multiple of every integer.

How is LCM used in real life?

Finding when repeating events coincide, for example two buses every 12 and 15 minutes both leave together every 60 minutes.

Related calculators

Greatest Common Factor CalculatorGCF/GCD of two or more numbers with steps.Prime Factorization CalculatorPrime factors, primality and divisors.Fraction CalculatorAdd, subtract, multiply and divide fractions and mixed numbers.