2017 · Q2
How many numbers from 1 to 1000 are divisible by 2,3,4 and 5 ?
Elementary MathematicsNumber System
- A16
- B17
- C32
- DNone of the above
Explanation
A number divisible by 2, 3, 4 and 5 must be a multiple of their LCM. Since 4 = 2², LCM(2,3,4,5) = 2²×3×5 = 60. The multiples of 60 from 1 to 1000 are ⌊1000/60⌋ = 16. Hence option (A) 16. (Trap: counting multiples of 2·3·5 = 30 gives 33; the factor 4 must be absorbed via the LCM.)