Question

Find the greatest number of four digits which is exactly divisible by each of 8, 12, 18 and 30.

Answer 1

8 = 1 × 2 × 2 × 2 = 2³
12 = 1 × 2 × 2 × 3 = 2² × 3¹
18 = 1 × 2 × 3 × 3 = 2¹ × 3²
30 = 1 × 2 × 3 × 5 = 2¹ × 3¹ × 5¹
LCM of 8, 12, 18, and 30 = 2³ × 3² × 5¹ = 360
Largest 4-digit number is 9999
Now, if we divide 9999 by 360, we will get 27.78 as quotient.
The integer just less than 27.78 is 27
∴ Required number = 360 × 27 = 9720
Hence, the greatest number of four digits which is exactly divisible by each of 8, 12, 18 and 30 is 9720.