GCF & LCM Practice
20 questions · 60 seconds · GCF & LCM of number pairs
Free · no login · instant feedback on every answer
Drill the two skills every fraction problem secretly runs on: greatest common factor and least common multiple. Twenty questions in sixty seconds alternate between finding the GCF of a pair like 12 and 18 and the LCM of a pair like 6 and 8, with instant feedback after every answer.
These two ideas are mirror images — the GCF is the biggest number that divides into both, the LCM is the smallest number both divide into — and they power the two hardest moves in fraction arithmetic. Simplifying 12/18 means dividing by the GCF; adding fractions with unlike denominators means rewriting over the LCM. Students who can produce either one in a few seconds stop losing fraction problems to the setup step.
Tips That Make It Stick
- List, then compare. For the GCF of 12 and 18, list each number's factors and take the largest one they share: 12 gives 1, 2, 3, 4, 6, 12 and 18 gives 1, 2, 3, 6, 9, 18 — the winner is 6.
- Walk the bigger number's multiples. For the LCM of 6 and 8, count by the larger number and stop at the first multiple the smaller one also divides: 8, 16, 24 — done. It is faster than listing both rows of multiples.
- Know the special cases. When one number divides the other, the answers are instant: the GCF is the smaller number and the LCM is the larger. GCF of 6 and 18 is 6; LCM is 18.
Frequently Asked Questions
What is the difference between GCF and LCM?
The greatest common factor is the largest number that divides evenly into both numbers, so it is never bigger than either of them. The least common multiple is the smallest number both divide into, so it is never smaller than either. GCF of 12 and 18 is 6; their LCM is 36.
Why do students need GCF and LCM for fractions?
Simplifying a fraction means dividing the top and bottom by their GCF (12/18 becomes 2/3 after dividing by 6), and adding fractions with unlike denominators means rewriting both over the LCM of the denominators. Weakness with GCF and LCM is the most common reason fraction arithmetic feels hard.
What grade learns GCF and LCM?
Greatest common factor and least common multiple are typically taught in 5th and 6th grade, right when students need them for simplifying fractions and adding fractions with unlike denominators.
📝 Matching Printable Worksheets
Prefer paper practice? These free PDF worksheets cover the same skill — each includes an answer key: