Question

Find the least number of five digits which is exactly divisible by each of 8, 12, 18, 40 and 45

Answer 1

8 = 1 × 2 × 2 × 2 = 2³
12 = 1 × 2 × 2 × 3 = 2² × 3¹
18 = 1 × 2 × 3 × 3 = 2¹ × 3²
40 = 1 × 2 × 2 × 2 × 5 = 2³ × 5¹
45 = 1 × 3 × 3 × 5 = 3² × 5¹
LCM of 8, 12, 18, 40 and 45 = 2³ × 3² × 5¹ = 360
Smallest five digit number is 10000
Now, if we divide 10000 by 360, we will get 27.78 as quotient.
The integer just greater than 27.78 is 28
∴ Required number = 360 × 28 = 10080
Hence, the least number of five digits which is exactly divisible by each of 8, 12, 18, 40 and 45 is 10080.