LCM Calculator
Calculate the Least Common Multiple (LCM) of up to 10 numbers instantly. Ideal for finding massive common denominators, complete with a step-by-step prime factorization breakdown.
How Does Prime Factorization Work?
There are several ways to find the Least Common Multiple (LCM). You can sit there and write out the times tables for every number until you find a match, but this becomes mathematically impossible once numbers get into the hundreds. The foolproof, professional method used by algebra students worldwide is Prime Factorization.
The Prime Factor Method: Example (LCM of 12 and 15)
Step 1: Break them down
Find all prime numbers that multiply to make your target number.
- 12 = 2² × 3
- 15 = 3 × 5
Step 2: Collect the highest powers
Look at all the prime bases (2, 3, and 5). Take the absolute highest exponent attached to each base across both numbers.
- The highest power of 2 is 2² (from the 12)
- The highest power of 3 is 3¹ (both have one)
- The highest power of 5 is 5¹ (from the 15)
Step 3: Multiply them together
Multiply your collected powers to get your final LCM.
Real-World Scheduling Examples
LCM is the backbone of logistics and rotational scheduling.
- Planetary Orbits: If Planet A takes 2 years to orbit the sun, and Planet B takes 5 years, the LCM dictates they will align every 10 years.
- Factory Belts: If a gear has 8 teeth turning against a gear with 12 teeth, the specific teeth that touched on rotation 1 won't touch again until exactly 24 teeth have passed (the LCM of 8 and 12).
Frequently Asked Questions
Solving Heavy Algebra Fractions?
Share this Least Common Multiple calculator with your classmates to instantly find the lowest common denominator for any polynomial.
Suggested hashtags: #Algebra #LCM #MathHelp #StudyTools #thecalcs