Listing Multiples
Write out multiples of each number and circle the smallest one they share. The most intuitive way to build understanding.
Free calculator for students & teachers
Find the Least Common Multiple,
Learn more
Find the Least Common Multiple,
instantly.
A free LCM calculator with step-by-step explanations, built for students and loved by teachers. Enter up to 10 numbers and see three ways to reach the answer.
Example preview
LCM =
60
Enter numbers above and press Calculate to see your answer.
Step-by-step solution
Example with 12 and 15:
- Multiples of 12: 12, 24, 36, 48, 60
- Multiples of 15: 15, 30, 45, 60
The smallest common multiple is 60.
The concept
What is the least common multiple?
The Least Common Multiple (LCM) of two or more whole numbers is the smallest positive number that every one of them divides into evenly. It is also known as the lowest common multiple.
For example, the LCM of 4 and 6 is 12, the smallest number that both 4 and 6 divide with no remainder.
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Adding fractions with different denominators.
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Scheduling events that repeat on different cycles.
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Music rhythms that line up after so many beats.
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Machines & signals with different periods.
Three approaches
Find the LCM, your way.
Three proven methods for different problems. Pick the one that matches your numbers.
Prime Factorization
Break each number into primes, take the highest power of each, then multiply. Shows why the LCM works, not just what it is.
GCD Formula
Use the Euclidean shortcut: (a × b) ÷ GCD(a, b). Works instantly on huge numbers where listing would take forever.
LCM in the wild
Where LCM actually matters.
Beyond the textbook, the least common multiple pops up in biology, music, and machinery.
The Cicada Puzzle
Two broods of cicadas emerge every 13 and 17 years. How often do they meet?
Music Rhythms
A drummer plays every 6 beats, a pianist every 8. When do they land together?
Gears & Cycles
Two gears with 12 and 18 teeth. How many turns until they reset to the start?
Three quick steps
How to use this calculator.
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01
Type your numbers
Enter up to 10 positive whole numbers, separated by commas, spaces, or new lines.
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02
Pick a method
Listing multiples, prime factorization, or the GCD formula. Pick whichever you want to learn.
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03
Get step-by-step
See the full working out: colored prime factors, pair-wise GCD, or a visual multiples list.
Loved by learners
What students & teachers say.
“The prime factorization view made it finally click for my class. I use it in every fractions lesson.”
Priya R.
Math Teacher · Grade 6
“I used to dread homework. Now I actually understand what LCM means. The colored pills helped so much.”
Ahmed K.
Student · 8th grade
“Fast, clean, and the dark mode looks beautiful on my laptop at night. Bookmarked.”
Maria L.
Self-learner · College prep
Questions?
Frequently asked.
What is the least common multiple?
The LCM of two or more integers is the smallest positive integer that is divisible by every one of them.
How do I calculate LCM by hand?
Use one of three methods: listing multiples, prime factorization, or the formula LCM(a,b) = (a × b) ÷ GCD(a,b).
What's the difference between LCM and GCD?
GCD is the largest number that divides the inputs. LCM is the smallest number that the inputs divide into. They are linked: LCM × GCD = a × b.
Can the LCM be smaller than the input numbers?
No. The LCM is always at least as large as the biggest input number.
Is "lowest common multiple" the same as LCM?
Yes, they mean exactly the same thing and are used interchangeably.