LCM Calculator
Work out the Least Common Multiple of 2 to 10 numbers with complete step-by-step working — prime factorization, a GCD cross-check, a multiples table, and how it sets up a fraction's common denominator.
2-10
Numbers Supported
3
Solving Methods
Live
Instant Results
🔢 Enter Numbers
Enter 2-10 positive integers. Click + to add more numbers.
Quick Examples
Least Common Multiple
36
LCM of: 12, 18
6
GCD
216
GCD × LCM
36
LCM
6
GCD
6
LCM ÷ GCD
No
Is LCM = Product?
Prime Factorization Breakdown
Step-by-Step Solution
List the numbers
12, 18
Prime factorize each number
12 = 2^2 × 3
18 = 2 × 3^2
For each prime, take the highest power seen
2^2: highest power across all numbers
3^2: highest power across all numbers
Cross-check with the GCD formula (2 numbers only)
GCD(12, 18) = 6
LCM = (12 × 18) / GCD(12, 18) = 216 / 6 = 36
Multiply the highest powers together
LCM = 2^2 × 3^2 = 36
Verify: LCM ÷ each number is a whole number
36 ÷ 12 = 3
36 ÷ 18 = 2
Multiples Table — Finding the First Common Multiple
| Number | ×1 | ×2 | ×3 | ×4 | ×5 | ×6 | ×7 | ×8 | ×9 | ×10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 |
| 18 | 18 | 36 | 54 | 72 | 90 | 108 | 126 | 144 | 162 | 180 |
First common multiple: 36
LCD — Adding Fractions with These Denominators
36
LCD (= LCM)
12, 18
Numbers as Denominators
1/12 = 3/36
multiply by 3
1/18 = 2/36
multiply by 2
3/36 + 2/36 = 5/36
sum of 1/n for each number, expressed over the shared LCD
Bonus stat: GCF(12, 18) × LCM = 6 × 36 = 216 = 12 × 18. Need the full GCF breakdown instead? Try our GCF calculator.
What Is the Least Common Multiple (LCM)?
The Least Common Multiple of two or more whole numbers is the smallest positive integer that every one of those numbers divides into evenly. It shows up any time you need a shared unit for numbers that don't naturally line up — most commonly when adding or subtracting fractions with different denominators, and when figuring out how long until two repeating events coincide (say, one task that repeats every 4 days and another every 6 days will next fall on the same day after 12 days, the LCM of 4 and 6). Don't confuse it with the Greatest Common Factor, which finds the largest number that divides evenly into your numbers rather than the smallest number they all divide evenly into — see our GCF calculator for that side of the relationship.
LCM Calculation Methods
Method 1 — Prime Factorization: factor each number, take the highest power of every prime that appears, then multiply. LCM(12, 18): 12 = 2²×3, 18 = 2×3² → LCM = 2²×3² = 4×9 = 36Method 2 — GCD Formula (two numbers only): LCM(a, b) = (a × b) ÷ GCD(a, b). LCM(12, 18) = (12×18) ÷ GCD(12,18) = 216 ÷ 6 = 36Method 3 — Listing Multiples: write out the multiples of each number until one repeats in every list. Multiples of 12: 12, 24, 36, 48… Multiples of 18: 18, 36, 54… → first common value: 36All three methods above always agree — this calculator runs the prime-factorization method as its primary engine and cross-checks it against the GCD formula whenever you enter exactly two numbers, so you can see both routes land on the same answer.
— FAQ