2018 · Q1
The highest four-digit number which is divisible by each of the numbers 16, 36, 45, 48 is
Elementary MathematicsHCF and LCM
- A9180
- B9360
- C9630
- D9840
Explanation
LCM(16, 36, 45, 48) = 2^4 x 3^2 x 5 = 720, since 16 = 2^4, 36 = 2^2 x 3^2, 45 = 3^2 x 5 and 48 = 2^4 x 3. The required number must be a multiple of 720. The highest four-digit multiple of 720 is 13 x 720 = 9360 (since 9999 / 720 = 13.88...). Hence option B.