Least common multiple (LCM) worksheets
Find the smallest number that each number divides into. Two numbers for beginners, three numbers for a challenge — with an answer key for every sheet.
How to solve them
- List the multiples of each number: 4, 8, 12, 16 … and 6, 12, 18 …
- The first number that appears in every list is the LCM (here 12).
- For bigger numbers, use prime factors: multiply the highest power of each prime that appears.
Ready-to-print least common multiple (lcm) worksheets
Nine fixed sets — three per level. Each PDF has the problems followed by the answer key.
Levels
| Level | Problems | Grade |
|---|---|---|
| Easy | Two numbers from 2 to 10 | 4–5 |
| Medium | Two numbers from 4 to 24 (LCM up to 300) | 6 |
| Hard | Three numbers from 2 to 15 | 6 |
Where LCM is used
The least common multiple is the least common denominator when adding or subtracting fractions with unlike denominators. It also answers everyday puzzles: if one bus comes every 6 minutes and another every 8, they leave together every 24 minutes.
Charts that help
- Multiplication chart 1–12 — free printable PDF
- Number chart 1–100 — free printable PDF
More math generators: multiplication, long division, comparing fractions, multiplying fractions, adding fractions, greatest common factor (gcf), area, place value, addition, subtraction, combining like terms. Or print a whole grade: 4th, 5th and 6th grade math.
Frequently asked questions
What's the difference between LCM and GCF?
The LCM is the smallest number both numbers divide into (it's at least as big as the larger number). The GCF is the biggest number that divides both (it's at most as big as the smaller number).
Is the LCM of two numbers always their product?
Only when they share no common factor, like 4 and 9 (LCM 36). For 4 and 6 the product is 24 but the LCM is 12.
Is there an answer key?
Yes. The PDF always ends with an answer key for the same problems, so you can print the questions for students and keep the key. Every answer is checked by automated tests.
Can I print the same worksheet again later?
Yes. Every sheet has a set number (the seed) printed in the footer and saved in the page address. Open the same link, or type the same level, count and set number, and you get exactly the same problems and answer key.