I can compute both, I just pick the wrong one about half the time.
Accepted answer
Ask whether you're **breaking something apart** or **waiting for things to line up**.
**GCF (greatest common factor)** — splitting into equal groups, or making something smaller. The answer is never bigger than your numbers.
- "What's the largest number of identical gift bags I can make from 24 pencils and 36 erasers?" → GCF(24, 36) = 12.
- Simplifying fractions: divide top and bottom by the GCF.
**LCM (least common multiple)** — events repeating until they coincide, or combining. The answer is never smaller than your numbers.
- "One bus comes every 12 minutes, another every 18. When do they arrive together?" → LCM(12, 18) = 36.
- Adding fractions: the common denominator is the LCM.
Quick sanity check: if your answer is *smaller* than the numbers you started with, you found a factor; if *larger*, a multiple. Compare that against what the question actually asked for.