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.