What is the smallest number divisible by 3 & 5, and leaves a remainder of 3 when divided by 8.
Solving:
Arranging the clues in a logical order:
- Number is divisible by 3 & 5
- Number when divided by 8 has a remainder of 3
From clue (1), the unknown number must be a multiple of the LCM of 3 & 5, so the unknown number must be a multiple of 15
From clue (2), the unknown number is also a multiple of 8 and has 3 added to it.
So let us make 2 charts from clue (1) & clue (2):
| Multiples of 15 | Multiple of 8 | Add 3 | |
| 15 | 8 | 11 | |
| 30 | 16 | 19 | |
| 45 | 24 | 27 | |
| 60 | 32 | 35 | |
| 75 | 40 | 43 | |
| 90 | 48 | 51 | |
| 105 | 56 | 59 | |
| 64 | 67 | ||
| 72 | 75 |
From this chart, 75 happens to be a multiple of 15, and when divided by 8 it has a remainder of 3.
Answer: 75.
You will find these sort of math puzzles in various math competitions like Perennial Math, Math Olympiad, Noetic Learning Math Contest, MathCounts, MOEMS Math Olympiad, U.S.A Mathematical Talent Search (USAMTS), Purple Comet Math, Math League, American Regions Mathematics League (ARML) & others.