Common Denominator Workshop Game
Convert pairs or triples of fractions to one least common denominator using exact equivalent numerators.
Math puzzle challenges
Loading fraction challenge…
Instructions, device progress and accessibility
Choose Practice or UTC Daily mode and select a difficulty. Use keyboard, touch, Tab, and Enter with the controls. Wrong checks reduce score; Hint and Undo mark assisted rounds. There is no required sign-in, and results remain on this device.
Local progress is checked when play begins.
Common Denominator Workshop — Rules, Examples and Help
Convert pairs or triples of fractions to one least common denominator using exact equivalent numerators.
How to play Common Denominator Workshop
Read the two or three given fractions. Enter the smallest positive whole number that is divisible by every original denominator in the LCD box. Then write a new numerator above that LCD for each original fraction. Every conversion must preserve the original fraction value. Select Check answer only after filling all fields. A denominator that is merely common, but not the least common multiple, does not meet this particular challenge.
What is the least common denominator?
The least common denominator is the least common multiple of the denominators. For example, the fractions 1/6 and 3/8 have denominators 6 and 8, whose least common multiple is 24. Converting 1/6 to twenty-fourths produces 4/24 because both parts are multiplied by four. Converting 3/8 to twenty-fourths produces 9/24 because both parts are multiplied by three. Their values have not changed.
Find the LCD step by step
List the multiples of each denominator until the first shared multiple is found, or use prime factorization to assemble the least common multiple. For denominators 4, 6 and 9, the LCD is 36 because 36 is divisible by 4, 6 and 9. Then multiply each original numerator by the factor required to turn its denominator into 36. If a denominator is already 36, its numerator does not change.
Mistakes to avoid
Adding denominators is not how the least common denominator is obtained. Multiplying all denominators gives a common multiple but may be larger than needed; for example, 6 × 8 = 48, yet the LCD is 24. When scaling a fraction, never multiply the denominator without also scaling the numerator. The checker uses exact integer relationships, which means there is no floating-point rounding or subjective judgment.
Common questions
Does it accept any shared denominator? No, this workshop specifically asks for the least common one. Do I need to simplify the original fractions first? No, use the displayed denominators as the inputs. Can I use a calculator to check multiples? Yes. Why are there three fractions on Hard? Their common denominator requires combining more than two divisibility constraints.