This LCM calculator finds the least common multiple of the integers on the page. Use it for adding fractions or aligning repeating schedules.
GCF and LCM relate through product identities for two positive integers. Compute GCF with the GCF calculator and compare factor lists on the common factor calculator.
Three ways to find the least common multiple
1. List multiples
Write out multiples of each number until one appears in every list. For 4 and 6: 4, 8, 12… and 6, 12… so the LCM is 12. This is fine for small numbers, but an LCM calculator is faster for large ones.
2. Prime factorization
Factor each number into primes. Take every prime that appears, raise it to the highest power it reaches in any one number, and multiply. This method scales well to three or more numbers.
3. Use the GCF
For two numbers, LCM(a, b) = |a × b| ÷ GCF(a, b). Wolfram MathWorld lists this identity with the formal definition. For three numbers, apply it in steps: LCM(a, b, c) = LCM(LCM(a, b), c).
LCM calculator worked example: 8, 12 and 18
Prime factors
- 8 = 2³
- 12 = 2² × 3
- 18 = 2 × 3²
The highest power of 2 is 2³ = 8, and the highest power of 3 is 3² = 9. LCM = 8 × 9 = 72.
Check with the GCF method
- GCF(8, 12) = 4, so LCM(8, 12) = 96 ÷ 4 = 24.
- GCF(24, 18) = 6, so LCM(24, 18) = 432 ÷ 6 = 72. ✔
A final check: 72 ÷ 8 = 9, 72 ÷ 12 = 6 and 72 ÷ 18 = 4, all whole numbers.
Using the LCM calculator result to add fractions
The least common denominator of several fractions is the LCM of their denominators. To add 3/8 + 5/12 + 1/18, rewrite each over 72: 27/72 + 30/72 + 4/72 = 61/72. Using the plain product 8 × 12 × 18 = 1,728 would also work, but you would then have to reduce a much larger fraction. The fraction calculator can confirm the sum.
Using an LCM calculator for repeating schedules
If one bus leaves every 12 minutes and another every 18, both leave together again after LCM(12, 18) = 36 minutes. The same logic applies to maintenance cycles, rotating shifts and gear teeth. The LCM is the first time all the cycles line up again.
LCM vs GCF, and common mistakes
- The LCM is never smaller than the largest input. The GCF is never larger than the smallest input. For any two positive numbers, LCM × GCF = a × b. For 12 and 18 that is 36 × 6 = 216.
- If one number divides the other, the LCM is the larger number: LCM(6, 18) = 18.
- If the numbers share no factor (they are coprime), the LCM is their product: LCM(8, 9) = 72.
- Don’t take the lowest prime powers. That gives the GCF instead.
LCM calculator for larger numbers
Listing multiples breaks down quickly for numbers like 84 and 90. Prime factors still work: 84 = 2² × 3 × 7 and 90 = 2 × 3² × 5, so the LCM is 2² × 3² × 5 × 7 = 1,260. Check: 84 × 15 = 1,260 and 90 × 14 = 1,260, and GCF(84, 90) = 6 gives 7,560 ÷ 6 = 1,260.
Last reviewed: October 2026