Question

Find the smallest 5-digit number which is exactly divisible by 20, 25, 30.

Answer 1

20 = 1 × 2 × 2 × 5 = 2² × 5¹
25 = 1 × 5 × 5 × 31 = 5²
30 = 1 × 2 × 3 × 5 = 2¹ × 3¹ × 5¹
LCM of 20, 25 and 30 = 2² × 3¹ × 5² = 300
Smallest five digit number is 10000
Now, if we divide 10000 by 60, we will get 33.33 as quotient.
The integer just greater than 33.33 is 34
∴ Required number = 300 × 34 = 10200
Hence, the smallest 5-digit number which is exactly divisible by 20, 25, 30 is 10200.