Least common multiple (LCM) calculator

The least common multiple (LCM) is the smallest positive number that every given number divides evenly. For 4, 6 and 10:

• Multiples of 4: 4, 8, 12, … 60 …
• Multiples of 6: 6, 12, 18, … 60 …
• Multiples of 10: 10, 20, 30, … 60 …

The first number on all three lists is 60, so LCM(4, 6, 10) = 60.

Listing multiples works for small numbers. The calculator uses prime factorization instead, which works for large numbers too, and shows its steps. It runs in your browser.

Factor each number into primes, then multiply every prime that appears, each with its highest exponent.

• 4 = 2²
• 6 = 2 · 3
• 10 = 2 · 5

Primes used: 2 (highest exponent 2), 3 and 5.

LCM = 2² · 3 · 5 = 60

Compare this with the GCF, which takes only shared primes with their lowest exponents.

For two numbers, LCM(a, b) = a × b / GCF(a, b).

Example: LCM(48, 180). The GCF is 12, so LCM = 48 × 180 / 12 = 720.

When you enter exactly two numbers, the calculator also shows the Euclidean algorithm for the GCF and this shortcut. You can find the GCF on its own with the GCF calculator.

• Adding fractions: the least common denominator is the LCM of the denominators. For 1/4 + 1/6, LCM(4, 6) = 12, so 3/12 + 2/12 = 5/12. The fraction calculator does this for you.
• Matching package sizes: hot dogs come in packs of 10 and buns in packs of 8. LCM(10, 8) = 40, so 4 packs of hot dogs and 5 packs of buns come out even.
• Schedules: one bus leaves every 12 minutes and another every 18 minutes. If they leave together now, they leave together again in LCM(12, 18) = 36 minutes.
• Gears and cycles: two gears with 12 and 30 teeth return to their starting alignment after LCM(12, 30) = 60 teeth have passed.

• The LCM is always at least as large as the largest number and at most their product.
• If two numbers are relatively prime (GCF 1), their LCM is simply their product: LCM(8, 15) = 120.
• If one number divides the other, the LCM is the larger number: LCM(6, 18) = 18.
• The calculator accepts numbers up to 12 digits; for very large inputs the LCM itself can exceed what can be shown exactly, and it warns you when that happens.

• Multiplying everything. 4 × 6 × 10 = 240 is a common multiple, but not the least one (60). It only works when the numbers share no factors.
• Using the lowest exponents. That gives the GCF. The LCM needs every prime at its highest power.
• Mixing up the two. A handy reminder: the least common multiple is a multiple, so it is at least as big as your largest number.

Quick check: your answer should divide evenly by every input. 60 ÷ 4 = 15, 60 ÷ 6 = 10 and 60 ÷ 10 = 6, so 60 works, and no smaller number does. If any division leaves a remainder, the answer is not a common multiple at all.