Bézout's identity provides yet another definition of the greatest common divisor "g" of two numbers "a" and "b". Consider the set of all numbers "ua" + "vb", where "u" and "v" are any two integers. Since "a" and "b" are both divisible by "g", every number in the set is divisible by "g". In other words, every number of the set is an integer multiple of "g". This is true for every common divisor of "a" and "b". However, unlike other common divisors, the greatest common divisor is a member of the set; by Bézout's identity, choosing "u" = "s" and "v" = "t" gives "g". A smaller common divisor cannot be a member of the set, since every member of the set must be divisible by "g". Conversely, any multiple "m" of "g" can be obtained by choosing "u" = "ms" and "v" = "mt", where "s" and "t" are the integers of Bézout's identity. This may be seen by multiplying Bézout's identity by "m",