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LCM of Three Numbers Calculator

Finding the Least Common Multiple of three numbers—like when adding three fractions or lining up three repeating schedules—requires care because two of the numbers can share a factor even when the third does not. Enter your three numbers below to see the exact solution.

Exact BigInt math
LCM of Three Numbers Result
LCM(12, 18, 24) = 72
Greatest Common Factor: GCF(12, 18, 24) = 6
Check the answer (every division leaves a remainder of 0):
72 ÷ 12 = 672 ÷ 18 = 472 ÷ 24 = 3

Show the Working (Step-by-Step)

Switch method in one click:

Step 1: Break each number down into its prime factors.

Write each input as a product of prime numbers, then group matching primes with exponents.

12 = 2 × 2 × 3
= 2² × 3
18 = 2 × 3 × 3
= 2 × 3²
24 = 2 × 2 × 2 × 3
= 2³ × 3

Step 2: For each prime, pick the highest exponent that appears in any single number.

PrimeIn 12In 18In 24Highest Power
22²2¹2³2³ = 8
33¹3²3¹3² = 9

Step 3: Multiply those highest prime powers together to get the LCM.

LCM = 2³ × 3² = 8 × 9 = 72

Why the Cake / Ladder Method Is So Popular for Three Numbers

When you use the division ladder (Tab 4 in the calculator above) on three numbers like , you write all three numbers in a row and divide by any prime that goes into at least two of them. If a prime only divides two of the three numbers, you simply carry the third number down unchanged:

  • Start with 6, 8, 12. All three are even, so divide by 2 to get 3, 4, 6.
  • In 3, 4, 6, both 4 and 6 are still even! Divide by 2 again and carry the 3 down to get 3, 2, 3.
  • In 3, 2, 3, two numbers are divisible by 3. Divide by 3 and carry the 2 down to get 1, 2, 1.
  • Multiply the divisors on the left by the bottom row: 2 × 2 × 3 × 1 × 2 × 1 = 24.

Need to compare 4, 5, or up to 10 numbers at once? Use our Main LCM Calculator.