This page makes free printable GCF and LCM worksheets on demand: press the button and you get a new sheet of 20 problems with a matching answer key, ready for US Letter or A4 paper. The version loaded below opens with items in the shape of LCM of 6 and 15 and LCM of 10 and 8; the key lists 30 and 40 next to their question numbers.
‘New set of problems’ opens the generator in its own tab. There you can change the problem count and turn the answer key on or off. ‘Print or save as PDF’ opens the print dialog — choose Save as PDF in the printer list to keep the file. The sheet fits US Letter and A4, and the answer key prints on its own page.
This sheet uses pairs built from factors 2 to 6, small enough to be listed out and large enough to make listing a slow method, and a typical line looks like LCM of 20 and 30.
Factors and multiples pull in opposite directions: factors divide into a number, multiples are built from it. A question like LCM of 6 and 15 answers 30, and knowing which direction the question is asking is half the battle.
Because each sheet is new, the child cannot recall the answer from having done the same pair yesterday.
Divisibility rules are worth memorising alongside this — even, digit sum divisible by three, ends in zero or five — because they turn LCM of 10 and 8 from a search into a glance.
In US classrooms these GCF and LCM worksheets are commonly aligned with the number system strand for grades 5 and 6, though the exact wording varies from state to state.
| # | Problem | Answer | What to check |
|---|---|---|---|
| 1 | LCM of 6 and 15 = | 30 | Watch for: stopping at a common factor rather than the greatest |
| 2 | LCM of 10 and 8 = | 40 | Check: missing one in a factor list |
| 3 | GCF of 18 and 9 = | 9 | Look at: swapping factor and multiple |
| 4 | LCM of 15 and 18 = | 90 | Ask about: leaving the factorisation incomplete |
| 5 | LCM of 20 and 30 = | 60 | Watch for: multiplying the two numbers for the lcm |
| 6 | LCM of 24 and 18 = | 72 | Check: treating a prime as having no factors |
Work LCM of 15 and 18 out loud as a demonstration. It gives 90. Children who hear LCM of 15 and 18 reasoned through once at the start of a session make noticeably fewer errors in the ten minutes that follow.
The item LCM of 10 and 8 is worth doing slowly. The answer to LCM of 10 and 8 is 40, and the route to it is the route every other problem on this sheet takes — which is why the sheet has 20 of them rather than one.
Keys are produced by the same code that produces the questions, so a mismatch between question and answer is not possible on these sheets.
The key prints on its own page by default. Uncheck the answer-key box before printing if you would rather keep it back and mark the sheet yourself.
Portrait orientation is what the sheet is designed for. Landscape works but wastes about a third of the paper, so leave the orientation alone unless you have a reason.
Printing works the same on US Letter and A4, because the layout uses relative widths rather than fixed inches. Set margins to default and scaling to 100%, and all 20 problems fit.
One sheet of GCF and LCM worksheets a day for two weeks will tell you more about where a child working at this level actually stands than any single long assessment.
Free printable math worksheets from a working math academy director in Korea. Problems come from our own code, not from a published workbook. Every sheet prints on US Letter or A4 with its answer key. All worksheets · Worksheet generator · Korean site
Last updated: 2026-09-13