Fraction Addition & Subtraction
Practice fraction addition and subtraction with a free, browser-based math game. Includes step-by-step strategy, common mistakes, and classroom tips.
MathGCF & LCM
The two operations behind simplifying fractions and finding common denominators. Below: fast methods and the mix-up that costs most points.
Choose your difficulty
Pick a level to start playing. You can switch at any time.
How to play
Read whether the GCF or the LCM is asked for, work it out, then tap the correct value.
Tip: your progress and best score are saved in this browser only.
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MathWhat you are actually practicing
Two numbers always share a largest common divisor and a smallest common multiple, and being able to find both quickly unlocks a surprising amount of later mathematics. The greatest common factor (GCF) is the biggest number that divides both, and it is what you use to simplify a fraction in one step. The least common multiple (LCM) is the smallest number both divide into, and it is the common denominator you want when adding fractions.
This game trains both directions, because students routinely mix them up: the GCF is never larger than the smaller number, while the LCM is never smaller than the larger one. That single fact eliminates most wrong answers immediately.
How the game works
You are given two numbers and asked for their GCF or their LCM. Four choices, a countdown, and an immediate reveal when you miss. Your score and best score stay in this browser only.
Easy asks for the GCF of small numbers. Medium mixes in the LCM. Hard uses larger pairs and both operations, so you must read the label before calculating.
Strategies that actually move your score
Use the size test first. The GCF cannot exceed the smaller number; the LCM cannot be smaller than the larger number. If an option breaks that rule, it is wrong no matter how plausible it looks.
For the GCF, list factors of the smaller number and work down. Check the larger divisors first, since you want the greatest. Stop at the first one that also divides the larger number.
For the LCM, list multiples of the larger number and work up. Stop at the first multiple the smaller number divides into. This is almost always faster than multiplying and dividing.
Lean on the product relationship. For any two numbers, GCF × LCM = a × b. If you have one, the other follows by division — a useful cross-check when time allows.
Common mistakes, and the fix for each
Mistake: answering the LCM when the GCF was asked. The fix is to point at the label before calculating.
Mistake: stopping at a common factor that is not the greatest. 12 and 18 share 2 and 3 and 6; the answer is 6. The fix is to keep checking downward from the larger candidates.
Mistake: multiplying for the LCM when one number already divides the other. The LCM of 4 and 8 is 8, not 32. The fix is the upward multiples list, which finds 8 immediately.
A short, honest FAQ
Do I need to install anything? No. It runs in any modern browser.
Why does this matter? Simplifying fractions, finding common denominators, and later algebra all reduce to these two operations.
What age is it for? Roughly grades 5 through 8.