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

To do: Find the smallest 5 digit number which is exactly divisible by 20,25 and 30.

Solution

To find the least 5 digit number which is exactly divisible by 20, 25 and 30, we

have to first find the LCM of 20, 25 and 30

20 = 2$\times$2$\times$5

25 = 5$\times$5

30 = 2$\times$3$\times$5

LCM = 2$\times$2$\times$3$\times$5$\times$5 = 300

So, LCM of 20, 25 and 30 is 300. But we want the least 5 digit number, which is exactly divisible by 20, 25 and 30. 

Least 5 digit number = 10000.

10000 = 33$\times$300 + 100

Next higher quotient is 34.

So, the required number = 34$\times$300 

= 10,200

Hence, the required number is 10,200, which is exactly divisible by 20, 25 and 30.