A and B are groups with binary operations and ?

Prove that the order of is

The binary operation of is define as such:

Let and .

Do I need to define the gcd as well? Regardless if I do or not, I am not sure where to proceed next.

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- September 9th 2011, 08:20 PMdwsmith|a\times b| = LCM[|a|, |b|]
A and B are groups with binary operations and ?

Prove that the order of is

The binary operation of is define as such:

Let and .

Do I need to define the gcd as well? Regardless if I do or not, I am not sure where to proceed next. - September 9th 2011, 10:35 PMfatpolomanjrRe: |a\times b| = LCM[|a|, |b|]
LCM(n, m) is the smallest integer that is both a multiple of both n and m. By definition the order of is the least such integer with . By definition of the order of a and b, we know that and . Therefore, k is the least such integer such that k = and k = (these expressions come from definition of n "divides" k, or "n | k"). This means, overall, that k is the least such integer that is a multiple of both n and m.