Question

find the smallest 4 digit number and largest 5 digit number which is exactly divisible by 75 and 125 respectively

Answer 1

First we find out the lowest number , which is exactly divisible by 15, 12, & 25..

ie, we have to find out the LCM of these numbers 15= 3x5

12 = 2²x3

25= 5²

So, LCM= 2²x3x 5² = 300

Now we can say that, 300 & all its multiples are divisible by 15,12,& 25

Now question is which multiple is to be considered…

Question is the largest 5 digit number divisible by all these numbers…

We know, 99999 is the largest 5digit number, but it's not divisible by 15,12,25

99999 is divided by 300, quotient= 333 & remainder= 99

99999–99= 99900 , which is 333rd multiple of 300.

So 333rd multiple of 300 will be divisible by 15,12,25.

333rd multiple of 300 = 99900

334th multiple will have 6digits in it…

So ANSWER = 99900