The use of the word 'or' means that the smallest positive integer is 6, as 6 ÷ 4 leaves a remainder of 2.
If you mean the smallest positive integer what when divided by both 4 and 9 leaves a remainder of 2 then the answer is 38.
4x + 2 = M : 4x = M - 2
9y + 2 = M : 9y = M - 2
4x = 9y : x = 9y/4: x = 2.25y
This means that for x to be an integer, y must = 4 or a multiple of 4.
Thus, if y = 4 then 9y + 2 = 36 + 2 = 38
And, x = 9
If higher value integers were required then put y = 8,( or higher multiples of 4)
Then 9y + 2 = 72 + 2 = 74
And, x = 18
234568
45
11.7778
Bn = 37n+1, where n is a positive integer from 1 to infinity, therefore there exists an infinite number of numbers that can be divided into 37 and leave 1 as a remainder
6.
6172839
85
234568
5
41
The integer is 157. 157/3 = 52 remainder 1 157/5 = 31 remainder 2 157/7 = 22 remainder 3
12
0, 1, 2, or 3.
41
The number zero is not the smallest positive integer. The number one is the smallest positive integer.
The lowest common multiple of a set of numbers is the smallest positive integer which can be evenly divided by each number in the set. It is, thus, the smallest number which belongs to the times-table of the each number in the set.
Because 63 is the smallest positive integer that both of those numbers divide into evenly with no remainder.