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LCM Calculator (Least Common Multiple)

Enter two or more whole numbers to get their least common multiple — the smallest number they all divide into. The steps use the fast GCF method, folding the list pair by pair.

How the LCM is found

The fastest method uses the greatest common factor: multiply the two numbers and divide by their GCF. For more than two numbers, fold pairwise — LCM of the first pair, then LCM of that with the next number:

For small numbers you can also list multiples of the largest number until one is divisible by the others, or merge prime factorizations taking each prime at its highest power (12 = 2²·3, 18 = 2·3² → LCM = 2²·3² = 36).

lcm(a, b) = a × b ÷ gcf(a, b)
lcm(a, b, c) = lcm(lcm(a, b), c)

Worked examples

Example 1: LCM of 4 and 6

Find the least common multiple of 4 and 6.

  1. Find the GCF first.
    GCF(4, 6) = 2
  2. Multiply the numbers and divide by it.
    (4 × 6) ÷ 2 = 12

LCM(4, 6) = 12. (Check the multiples: 4, 8, 12… and 6, 12… meet at 12.)

Example 2: common denominator for fractions

Add 5/12 + 7/18 — what's the common denominator?

  1. The LCD is the LCM of the denominators.
    GCF(12, 18) = 6; (12 × 18) ÷ 6 = 36
  2. Rewrite both fractions over 36.
    5/12 = 15/36; 7/18 = 14/36

LCD = 36, so the sum is 29/36.

Example 3: when do three buses meet?

Buses leave every 6, 10 and 15 minutes. They just left together — when next?

  1. Fold the first pair.
    LCM(6, 10) = 30
  2. Fold in the third.
    LCM(30, 15) = 30

In 30 minutes — the LCM of the three intervals.

FAQ

What's the relationship between LCM and GCF?+

For two numbers, LCM × GCF = a × b — they're complementary. The GCF collects the shared factors, the LCM covers all factors. Our GCF calculator shows the other half of the story.

What's the LCM of two coprime numbers?+

Their product. If the GCF is 1 (like 8 and 15), nothing is shared, so the LCM is 8 × 15 = 120.

Can the LCM be smaller than one of the numbers?+

Never — the LCM is a multiple of every input, so it's at least as large as the largest one. It equals the largest number exactly when all others divide it, e.g. LCM(5, 10, 20) = 20.

What is the LCM used for in real life?+

Anywhere cycles need to line up: common denominators for fractions, repeating schedules (buses, shifts, medication), gear rotations, and finding when patterns repeat together.

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