The multiples of 48 are 48, 96, 144, 192, 240, 288, 336, 384, 432, 480 and so on. According to MathWorld, the multiple of any number is that number times another integer.
An integer is any whole number. Because there is an infinite number of integers, there is also an infinite number of multiples. One way to test if a number (x) is a multiple of 48 is to divide x by 48. If the quotient is a whole number, then x is a multiple of 48.
It can also be helpful to view multiples in their relationship to factors. In an equation A x B = C, A and B are factors of C, and C is a multiple of A and B. For example, when you look at 48 x 2 = 96, the number 96 is a multiple of both 48 and 2, while the numbers 48 and 2 are both factors of 96.