LCM Calculator (Least Common Multiple)

The smallest positive number that every number in your list divides into exactly. Useful for common denominators and repeating schedules.

Find the LCM

At least two non-zero whole numbers, separated by commas or spaces.

Least common multiple60
Greatest common factor
2

Working

  1. 4 = 2²
  2. 6 = 2 × 3
  3. 10 = 2 × 5
  4. Take the highest power of every prime that appears and multiply: LCM = 60

How to find the LCM

Write each number as a product of primes, then multiply together the highest power of every prime that appears. For two numbers there is also a shortcut using the GCF:

lcm(a, b) = |a × b| ÷ gcd(a, b)

Worked example

LCM of 4, 6 and 10

  1. 4 = 2²
  2. 6 = 2 × 3
  3. 10 = 2 × 5
  4. Highest powers: 2², 3 and 5 → 4 × 3 × 5 = 60

LCM(4, 6, 10) = 60

Practical uses

  • Adding fractions: the least common denominator of 1/4 + 1/6 + 1/10 is 60.
  • Schedules: buses every 12 and 18 minutes leave together again after LCM(12, 18) = 36 minutes.
  • Gears and repeating patterns lining up again.