Hot dogs come 10 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?

2 packs of hot dogs and 5 packs of buns

Hot dogs come 14 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?

2 packs of hot dogs and 7 packs of buns

Hot dogs come 4 to a pack and buns come 13 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?

13 packs of hot dogs and 4 packs of buns

Least common multiple worksheet

Take every prime that appears, as many times as it appears in whichever number uses it most. That is the smallest number all of them go into, and it is what a common denominator is.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Least Common Multiple Date Period Find each least common multiple, or solve each problem. Find the least common multiple What is the smallest positive number that is a multiple of both $8$ and $2$ ? What is the least common multiple of $7$ and $2$ ? Buses on two routes leave a stop every 6 and 8 minutes. They leave together now. How many minutes later do they next leave together? Find the LCM of $8$ and $11$ . Two runners start together and finish a lap every 6 and 9 seconds. After how many seconds are they next at the start line together? Find the LCM of $2$ and $12$ . What is the least common multiple of $2$ and $10$ ? What is the smallest positive number that is a multiple of both $11$ and $2$ ? Plates come in packs of 3 and cups in packs of 2. What is the smallest number of plates you can buy to have exactly as many cups? What is the least common multiple of $9$ and $12$ ? Solve LCM word problems One bus leaves every 15 minutes and another every 6 minutes. Both leave at noon. In how many minutes do they next leave together? Hot dogs come 6 to a pack and buns come 5 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy? Hot dogs come 10 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible? Hot dogs come 10 to a pack and buns come 3 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy? Hot dogs come 14 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible? One bus leaves every 6 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together? Hot dogs come 7 to a pack and buns come 10 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy? Hot dogs come 4 to a pack and buns come 13 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible? One bus leaves every 12 minutes and another every 7 minutes. Both leave at noon. In how many minutes do they next leave together? One bus leaves every 11 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together? Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Least Common Multiple

Date Period

Find each least common multiple, or solve each problem.

Find the least common multiple
What is the smallest positive number that is a multiple of both $8$ and $2$ ?
What is the least common multiple of $7$ and $2$ ?
Buses on two routes leave a stop every 6 and 8 minutes. They leave together now. How many minutes later do they next leave together?
Find the LCM of $8$ and $11$ .
Two runners start together and finish a lap every 6 and 9 seconds. After how many seconds are they next at the start line together?
Find the LCM of $2$ and $12$ .
What is the least common multiple of $2$ and $10$ ?
What is the smallest positive number that is a multiple of both $11$ and $2$ ?
Plates come in packs of 3 and cups in packs of 2. What is the smallest number of plates you can buy to have exactly as many cups?
What is the least common multiple of $9$ and $12$ ?

Solve LCM word problems
One bus leaves every 15 minutes and another every 6 minutes. Both leave at noon. In how many minutes do they next leave together?
Hot dogs come 6 to a pack and buns come 5 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?
Hot dogs come 10 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?
Hot dogs come 10 to a pack and buns come 3 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?
Hot dogs come 14 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?
One bus leaves every 6 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together?
Hot dogs come 7 to a pack and buns come 10 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?
Hot dogs come 4 to a pack and buns come 13 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?
One bus leaves every 12 minutes and another every 7 minutes. Both leave at noon. In how many minutes do they next leave together?
One bus leaves every 11 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together?



Sigma Prep · sigmaprep.io/worksheets Name Least Common MultipleAnswer keyVersion 1 Date Period Find each least common multiple, or solve each problem. Find the least common multiple What is the smallest positive number that is a multiple of both $8$ and $2$ ? $8$ What is the least common multiple of $7$ and $2$ ? $14$ Buses on two routes leave a stop every 6 and 8 minutes. They leave together now. How many minutes later do they next leave together? $24$ Find the LCM of $8$ and $11$ . $88$ Two runners start together and finish a lap every 6 and 9 seconds. After how many seconds are they next at the start line together? $18$ Find the LCM of $2$ and $12$ . $12$ What is the least common multiple of $2$ and $10$ ? $10$ What is the smallest positive number that is a multiple of both $11$ and $2$ ? $22$ Plates come in packs of 3 and cups in packs of 2. What is the smallest number of plates you can buy to have exactly as many cups? $6$ What is the least common multiple of $9$ and $12$ ? $36$ Solve LCM word problems One bus leaves every 15 minutes and another every 6 minutes. Both leave at noon. In how many minutes do they next leave together? $30$ minutes Hot dogs come 6 to a pack and buns come 5 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?30 hot dogs and 30 buns Hot dogs come 10 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?2 packs of hot dogs and 5 packs of buns Hot dogs come 10 to a pack and buns come 3 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?30 hot dogs and 30 buns Hot dogs come 14 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?2 packs of hot dogs and 7 packs of buns One bus leaves every 6 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together? $24$ minutes Hot dogs come 7 to a pack and buns come 10 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?70 hot dogs and 70 buns Hot dogs come 4 to a pack and buns come 13 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?13 packs of hot dogs and 4 packs of buns One bus leaves every 12 minutes and another every 7 minutes. Both leave at noon. In how many minutes do they next leave together? $84$ minutes One bus leaves every 11 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together? $88$ minutes Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Least Common MultipleAnswer keyVersion 1

Date Period

Find each least common multiple, or solve each problem.

Find the least common multiple
What is the smallest positive number that is a multiple of both $8$ and $2$ ? $8$
What is the least common multiple of $7$ and $2$ ? $14$
Buses on two routes leave a stop every 6 and 8 minutes. They leave together now. How many minutes later do they next leave together? $24$
Find the LCM of $8$ and $11$ . $88$
Two runners start together and finish a lap every 6 and 9 seconds. After how many seconds are they next at the start line together? $18$
Find the LCM of $2$ and $12$ . $12$
What is the least common multiple of $2$ and $10$ ? $10$
What is the smallest positive number that is a multiple of both $11$ and $2$ ? $22$
Plates come in packs of 3 and cups in packs of 2. What is the smallest number of plates you can buy to have exactly as many cups? $6$
What is the least common multiple of $9$ and $12$ ? $36$

Solve LCM word problems
One bus leaves every 15 minutes and another every 6 minutes. Both leave at noon. In how many minutes do they next leave together? $30$ minutes
Hot dogs come 6 to a pack and buns come 5 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?30 hot dogs and 30 buns
Hot dogs come 10 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?2 packs of hot dogs and 5 packs of buns
Hot dogs come 10 to a pack and buns come 3 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?30 hot dogs and 30 buns
Hot dogs come 14 to a pack and buns come 4 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?2 packs of hot dogs and 7 packs of buns
One bus leaves every 6 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together? $24$ minutes
Hot dogs come 7 to a pack and buns come 10 to a pack. You want exactly as many hot dogs as buns. At the least, how many hot dogs and how many buns must you buy?70 hot dogs and 70 buns
Hot dogs come 4 to a pack and buns come 13 to a pack. You want exactly as many hot dogs as buns. How many packs of each should you buy, using as few packs as possible?13 packs of hot dogs and 4 packs of buns
One bus leaves every 12 minutes and another every 7 minutes. Both leave at noon. In how many minutes do they next leave together? $84$ minutes
One bus leaves every 11 minutes and another every 8 minutes. Both leave at noon. In how many minutes do they next leave together? $88$ minutes

How to do these

The LCM of $6$ and $8$

6 is 2 x 3, and 8 is 2 x 2 x 2.
Take three 2s and one 3.
That is 24.

The answer is $24$ .

Where students go wrong

Multiplying the two numbers together. That always gives a common multiple, but it is only the least one when the two share no factors; 6 times 8 is 48, and 24 gets there first.

Also called LCM, lowest common multiple or common denominator.

What you can put on this worksheet

The least common multiple: What is the smallest positive number that is a multiple of both $7$ and $8$ ? → $56$
Word problems: One bus leaves every 8 minutes and another every 3 minutes. Both leave at noon. In how many minutes do they next leave together? → $24$ minutes
Monomials: Find the LCM of $8 u^{2}, 7 u^{2} v$ → $56 u^{2} v$

Questions about these worksheets

Yes. Every least common multiple sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the least common multiple questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: the least common multiple, word problems and monomials. Tick as many as you want and set how many of each, or let it spread them evenly.

Multiplying the two numbers together. That always gives a common multiple, but it is only the least one when the two share no factors; 6 times 8 is 48, and 24 gets there first.

Least common multiple worksheet

Select your difficulty

Find the least common multiple

Solve LCM word problems

Find the least common multiple

Solve LCM word problems

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these least common multiple worksheets free?+

Do the least common multiple worksheets come with an answer key?+

Are these least common multiple worksheets printable?+

What grade are these least common multiple worksheets for?+

Can I get a different version of the same least common multiple worksheet?+

Is this a free alternative to Kuta Software for least common multiple?+

Can I choose how hard the least common multiple questions are?+

What kinds of question are on a least common multiple worksheet?+

What do students get wrong with least common multiple?+