| 释义 |
least common multiple For two non‐zero integers a and b, an integer that is a multiple of both is a common multiple. Of all the positive common multiples, the least is the least common multiple (lcm), denoted by [a,b] or lcm(a,b). The lcm of a and b has the property of dividing any other common multiple of a and b. If the prime decompositions of a and b are known, the lcm is easily obtained: for example, if a = 168 = 23×3×7 and b = 180 = 22×32×5, then the lcm is 23×32 × 5×7 = 2520. For positive integers a and b, the lcm is equal to ab/(a, b), where (a,b) is the greatest common divisor (gcd). The gcd can be efficiently found using the Euclidean Algorithm.
Similarly, any finite set of non‐zero integers, a1, a2,…, an has an lcm denoted by [a1, a2,…, an]. |