Question

what is the lowest positive integer greater than 1, which when divided by 5 or 8 leaves a remainder of 1?

Answer 1

41

Answer 2

\[\{\text{Mod}[41,5]=1,\text{ Mod}[41,8]=1\} \]

Answer 3

If you wanted to actually figure this out, find the least common multiple of 5 and 8, and add 1.

LCM of two numbers can be found by factoring each number, then taking the highest power of each unique factor found in either number. For example, the LCM of 25 and 45:

25 = 5^2
45 = 3^2*5

LCM = 3^2*5^2 = 9*25= 225

25 50 75 100 125 150 175 200 225
45 90 135 180 225

225 is the first number that is a multiple of both 25 and 45.

LCM of 5 and 8:
5 = 5^1
8 = 2^3

LCM(5,8) = 2^3*5^1 = 40
40 + 1 = 41 is the first number that will give a remainder of 1 when divided by either 5 or 8.

Answer 4

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