What does LCM stand for?

LCM stands for least common multiple. A multiple of 6 is any number you reach by counting in sixes: 6, 12, 18, 24 and so on. Common means the number is in both lists, and least means the smallest one. For 6 and 10, the common multiples are 30, 60, 90 and onward, so the LCM is 30. Many books call it the lowest common multiple, with the same meaning.

How do you find the LCM of two numbers?

For larger numbers, prime factors are the surest route. A prime is a number that only 1 and itself divide. Split each number into primes: 15 = 3 × 5 and 18 = 2 × 3 × 3. Take each prime as many times as it appears in whichever number has the most of it: one 2, two 3s and one 5. Their product, 2 × 3 × 3 × 5 = 90, is the LCM.

Is there a trick to check an LCM?

Yes: divide your answer by each of the two numbers, and both results must be whole. If a number bigger than 1 divides both results, your answer is a common multiple but not the least. For 8 and 20, the product 160 gives 20 and 8, which share 4, so divide 160 by 4. Then 40 gives 5 and 2, which share nothing but 1, so 40 is the LCM.

Why does my child just multiply the two numbers?

Multiplying always gives a common multiple, so it feels like a safe answer. It gives the least one only when nothing but 1 divides both numbers, as with 4 and 9, where 36 is right. For 4 and 10 it gives 40, yet 20 is already in both tables. Before multiplying, ask your child to count up in the bigger number and test the first few results.

Is this lowest common multiple practice free, and how can a class use it?

Yes, it is free on any school device with a web browser, with nothing to install and no pupil logins. Write a puzzle on the board: two buses leave school together, one every 10 minutes and one every 15. Pupils list each bus’s times in a row until one number appears in both rows: 30 minutes. The schools plan lets the teacher see on one dashboard which pupils find the LCM faster, and it is priced per student.

Math practice · reimagined

LCM Game

Numbers in this least common multiple game never go past 30, yet the biggest answer is 870, the LCM of 29 and 30. Find where both times tables meet before your rival, and your fighter strikes while the other is still counting.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What is the least common multiple?

The least common multiple, or LCM, of two numbers is the smallest number found in both of their times tables. The numbers in a times table are called multiples. Cups come in boxes of 6 and plates in boxes of 9. To have as many cups as plates, the fewest you can buy is 18 of each.

Every level of LCM

Example: the LCM of 9 and 12

The screen shows LCM(9, 12), so you need the smallest number that both 9 and 12 divide into exactly.
Count up in twelves, because the bigger number climbs faster: 12, 24, 36.
Test each one with 9: 12 and 24 leave a remainder, but 36 is exactly 4 × 9.
36 is the first number in both tables, so you type 36 on the keypad.

Learn it step by step

LCM means "least common multiple" — the smallest number that BOTH numbers divide into evenly.

For 4 and 6: count up in 4s (4, 8, 12…) and in 6s (6, 12…) — they first meet at 12. So lcm(4, 6) = 12. It's like two friends with different step sizes — when do they next land on the same spot?

Type the smallest shared multiple.

Tips and common mistakes

If one number divides the other, the bigger one is the LCM, as in LCM(3, 12) = 12. If only 1 divides both, multiply them: LCM(5, 7) = 35.
A common mistake is giving a number that divides both, like 5 for 10 and 15: that is a divisor. The LCM is never below the bigger number.
Count aloud at home: one person claps on every 3rd number, another stamps on every 4th. The first number with a clap and a stamp together is 12, the LCM.

How to play

You answer on the keypad with one number: the smallest that two others both divide into, so LCM(6, 7) wants 42. If the bigger number is already a multiple of the smaller, as in LCM(2, 10) or LCM(8, 8), it is the answer itself. Beat your rival to it and Pea Pod strikes; your speed decides how much it hurts.

— Quick answers —

LCM: the short FAQ

What does LCM stand for?: LCM stands for least common multiple. A multiple of 6 is any number you reach by counting in sixes: 6, 12, 18, 24 and so on. Common means the number is in both lists, and least means the smallest one. For 6 and 10, the common multiples are 30, 60, 90 and onward, so the LCM is 30. Many books call it the lowest common multiple, with the same meaning.
How do you find the LCM of two numbers?: For larger numbers, prime factors are the surest route. A prime is a number that only 1 and itself divide. Split each number into primes: 15 = 3 × 5 and 18 = 2 × 3 × 3. Take each prime as many times as it appears in whichever number has the most of it: one 2, two 3s and one 5. Their product, 2 × 3 × 3 × 5 = 90, is the LCM.
Is there a trick to check an LCM?: Yes: divide your answer by each of the two numbers, and both results must be whole. If a number bigger than 1 divides both results, your answer is a common multiple but not the least. For 8 and 20, the product 160 gives 20 and 8, which share 4, so divide 160 by 4. Then 40 gives 5 and 2, which share nothing but 1, so 40 is the LCM.
Why does my child just multiply the two numbers?: Multiplying always gives a common multiple, so it feels like a safe answer. It gives the least one only when nothing but 1 divides both numbers, as with 4 and 9, where 36 is right. For 4 and 10 it gives 40, yet 20 is already in both tables. Before multiplying, ask your child to count up in the bigger number and test the first few results.
Is this lowest common multiple practice free, and how can a class use it?: Yes, it is free on any school device with a web browser, with nothing to install and no pupil logins. Write a puzzle on the board: two buses leave school together, one every 10 minutes and one every 15. Pupils list each bus’s times in a row until one number appears in both rows: 30 minutes. The schools plan lets the teacher see on one dashboard which pupils find the LCM faster, and it is priced per student.

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