Question

Find the greatest number consisting of 6 digits which is exactly divisible by 24 15 36

Answer 1

Answer:

Step-by-step explanation:

Greatest number of 6 digits is 999999. now, the required number must be divisible by the LCM of 24,15 and 36.

by prime factorisation,

24=2³ × 3

15 = 3 × 5

36 = 2² × 3²

∴ LCM(24,15,36)= 2³×3²×5= 360

now divide 999999 by 360

∴ remainder = 279  

hence number required = 999999 - remainder when 999999 ÷ 360

⇒ 999999 - 279

⇒ 999720

∴ the required number is 999720.