Least Common Multiple (LCM) Calculator
Find the least common multiple of two or more numbers using prime factorization.
Returns step-by-step working for fractions and scheduling problems.
Least Common Multiple (LCM) is the smallest positive number that is evenly divisible by two or more given numbers. This calculator finds the LCM using the relationship between LCM and GCF (Greatest Common Factor).
Formula for two numbers:
LCM(a, b) = |a × b| / GCF(a, b)
The GCF is found using the Euclidean algorithm, which repeatedly divides the larger number by the smaller and takes the remainder until reaching zero. For three or more numbers, the LCM is calculated by chaining: LCM(a, b, c) = LCM(LCM(a, b), c).
What each variable means:
- a, b — the input numbers whose LCM you want to find.
- GCF(a, b) — the greatest common factor (also called GCD), the largest number that divides both a and b evenly.
When to use this calculator: Use it when adding or subtracting fractions (the LCM of the denominators gives the least common denominator). It is also useful for scheduling problems, such as finding when two repeating events will next occur at the same time.
Practical example: LCM of 12 and 8. First, find GCF(12, 8) = 4. Then LCM = (12 × 8) / 4 = 96 / 4 = 24. Verification: 24 / 12 = 2 and 24 / 8 = 3 — both divide evenly.
Another example with three numbers: LCM(4, 6, 10). LCM(4, 6) = 24 / 2 = 12. Then LCM(12, 10) = 120 / 2 = 60.
Common uses:
- Adding fractions with different denominators (finding the LCD)
- Finding when periodic events will coincide (bus schedules, shift rotations)
- Calculating gear ratios, musical rhythms, and repeating cycles
Tips: The LCM of two numbers is always at least as large as the bigger number. If the two numbers share no common factors (they are coprime), the LCM is simply their product. For example, LCM(7, 9) = 63.