What is the smallest natural number, greater than 1

Question

That has a remainder of one when divided by 2,5 or 18?

Answer 1

The required number will be one more than the least commmon multiple of 2,5 and 18. As LCM is divisible by these numbers and we want remainder 1, so we need to add 1 To the LCM 0f 2,5 & 18..

 

LCM of 2,5,18 =90

 

One more than LCM = 90+1=91

 

Therefore 91 is the smallest natural number that has remainder 1 when divided by 2,5 or 18

Answer 2

The number 2,5 is not a natural number, but the number the problem asks us to find must be a natural number.

 

The prime factors of 18 are 2*3*3.  And, 2.5 does not share any of these factors.  The smallest natural number that is evenly divisible by both 2.5 and 18 is their product, 45.  The smallest natural number that has a remainder of 1 when divided by 2.5 or 18 is 46 (it is a natural number) and

                  46/2.5 = 18 remainder 1

                  46/18 = 2.5 remainder 1