2020 · Q47
What is the least perfect square which is divisible by 3, 4, 5, 6 and 7?
Elementary MathematicsHCF and LCM
- A1764
- B17640
- C44100
- D176400
Explanation
LCM(3, 4, 5, 6, 7) = 420 = 2² × 3 × 5 × 7. For a perfect square every prime needs an even exponent, so multiply by 3 × 5 × 7 = 105: 420 × 105 = 44100 = 210², the least such square. Indeed 210² = 44100 is divisible by each of 3, 4, 5, 6 and 7.