5 min read
2026-03-07
GCD and LCM are not just abstract concepts. They solve specific practical problems.
What is the largest square tile that can be laid on a floor measuring 360 × 480 cm without cutting? Answer: GCD(360, 480) = 120 cm.
Two traffic lights switch at intervals of 40 and 60 seconds. After how many seconds will they coincide again? Answer: LCM(40, 60) = 120 seconds.
When adding fractions with different denominators, the LCM of the denominators gives the lowest common denominator. This makes calculations simpler.
You need to divide 48 apples and 36 oranges equally into the maximum number of baskets. GCD(48, 36) = 12 baskets, with 4 apples and 3 oranges each.
Polyrhythms in music are described using LCM. Two rhythms with periods of 3 and 4 beats will coincide after LCM(3, 4) = 12 beats.
Two gears with 24 and 36 teeth. After how many rotations of the small gear will they return to their starting position? LCM(24, 36) / 24 = 3 rotations.
Buses depart every 15 and 20 minutes. LCM(15, 20) = 60 — they will coincide every hour.
See also: Fraction Calculator, Prime Number Checker, Proportion Calculator