how do i do this mathematically.

Question

What is the smallest multiple of 75 that consists of just 1's and 0's?

Answer 1

this is the second time posting this; the first time it did not show ???

75=3*5*5

3*5*5*2*2=300 which gives us the 0's

any multiple of 100 divisible by 3 will be divisible by 75

the smallest number, that consists only of 1's, that is divisible by 3 is 111

replace the 3 in 300 with 111

you get 11,100

this is divisible by 75 because its prime factorization is 2*2*3*5*5*37 which contains 3*5*5

Answer 2

11,100  which is 148 x 75

 

I found this by trial and error

 

 

Answer 3

Answer removed. Repeating decimal not an answer.