🎓 Mathematics • Number Theory
100% Client-Side Privacy
LCM Calculator
Finds the least common multiple of two integers using the GCD relation formula with step-by-step math.
Fractions & Number Theory
Fractions, Primes & Factors Studio
Precision fraction reduction to lowest terms, primality tests, Sieve of Eratosthenes generator, divisor sums, and Euclidean GCD/LCM steps.
Input Integers
Preset Pairs:
Greatest Common Divisor
gcd(144, 84)
12
Least Common Multiple
lcm(144, 84)
1008
= (144 × 84) / 12
Euclidean Division Algorithm Proof
| Step | Dividend (a) | Divisor (b) | Quotient (q) | Remainder (r) |
|---|---|---|---|---|
| 1 | 144 | 84 | 1 | 60 |
| 2 | 84 | 60 | 1 | 24 |
| 3 | 60 | 24 | 2 | 12 |
| 4 | 24 | 12 | 2 | 0 |
What is the Least Common Multiple?
The LCM of two integers is the smallest positive integer that is divisible by both numbers.
Formula & Step-by-Step Calculation
lcm(a, b) = |a × b| / gcd(a, b)
Relationship between product, GCD, and LCM.
Worked Step-by-Step Examples
Example 1
LCM of 12 and 18
Solution: 36
• GCD(12, 18) = 6. LCM = (12 × 18) / 6 = 216 / 6 = 36.
Common Real-World & Academic Use Cases
- ✓ Finding common denominators for fractions
- ✓ Synchronizing repeating cycles and traffic lights
- ✓ Gearing rotations
How to Use the LCM Calculator
1
Input Integers
Enter two positive numbers.
2
Read LCM
Inspect calculated LCM and formula steps.
Frequently Asked Questions
Q: Why is LCM useful in fraction addition?
The LCM of two denominators is the Least Common Denominator (LCD).