🔢 最小公倍数计算器（多个数、质因数分解、最大公约数）LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD)
求 2–20 个正整数的最小公倍数（LCM）和最大公约数（GCD），列出每个数的质因数分解，并说明 LCM 取每个质因数的最高次幂。用空格、换行或逗号分隔（如 12 18 30）。大数用精确整数计算。本地处理。Least common multiple (LCM) and greatest common divisor (GCD) of 2–20 positive integers, with the prime factorisation of each and how the LCM takes the highest power of every prime. Separate numbers with spaces, line breaks or commas (e.g. 12 18 30). Exact integer arithmetic for large results. Processed locally.
使用说明与常见问题How-to & FAQ
「最小公倍数计算器（多个数、质因数分解、最大公约数）」是什么？What is the LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD) tool?
求 2–20 个正整数的最小公倍数（LCM）和最大公约数（GCD），列出每个数的质因数分解，并说明 LCM 取每个质因数的最高次幂。用空格、换行或逗号分隔（如 12 18 30）。大数用精确整数计算。本地处理。Least common multiple (LCM) and greatest common divisor (GCD) of 2–20 positive integers, with the prime factorisation of each and how the LCM takes the highest power of every prime. Separate numbers with spaces, line breaks or commas (e.g. 12 18 30). Exact integer arithmetic for large results. Processed locally.
如何使用「最小公倍数计算器（多个数、质因数分解、最大公约数）」？How do I use the LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD) tool?
在「最小公倍数计算器（多个数、质因数分解、最大公约数）」中，填写「整数（2–20 个）」等参数，结果会随输入实时计算并显示在下方。In the LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD): Fill in "Integers (2–20)"; results are recalculated instantly as you type.
怎样求几个数的最小公倍数？How do I find the LCM of several numbers?
把每个数分解质因数，取每个质因数出现过的最高次幂相乘。12 = 2² × 3，18 = 2 × 3²，30 = 2 × 3 × 5，所以 LCM = 2² × 3² × 5 = 180。Factor each number into primes and multiply the highest power of each prime that appears. 12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5, so LCM = 2² × 3² × 5 = 180.
能输入多少个数？How many numbers can I enter?
2–20 个，每个是 1 到 1,000,000,000,000 之间的整数；结果用精确大整数计算，不会丢位。2 to 20, each a whole number from 1 to 1,000,000,000,000; the result is computed with exact big integers, so no digits are lost.
能举个计算实例吗？Can you show a worked example?
例如在「最小公倍数计算器（多个数、质因数分解、最大公约数）」中填 整数（2–20 个） = 12 18 30，结果区显示：最小公倍数 LCM：180；最大公约数 GCD：6；12 =：2² × 3；18 =：2 × 3²；30 =：2 × 3 × 5；LCM 的质因数：2² × 3² × 5；ℹ LCM 取每个质因数在各数中的最高次幂相乘；两个数时 LCM × GCD = 两数之积For example, entering Integers (2–20) = 12 18 30 in the LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD) gives: Least common multiple (LCM): 180; Greatest common divisor (GCD): 6; 12 =: 2² × 3; 18 =: 2 × 3²; 30 =: 2 × 3 × 5; LCM prime factors: 2² × 3² × 5; ℹ the LCM multiplies the highest power of each prime found in any number; for two numbers LCM × GCD = their product
有哪些选项可以调整？What options can I adjust?
「最小公倍数计算器（多个数、质因数分解、最大公约数）」的设置：「整数（2–20 个）」默认 12 18 30。每次生成结果都按当前设置处理。Settings in the LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD) — "Integers (2–20)" default 12 18 30. The result always uses the current settings.
「最小公倍数计算器（多个数、质因数分解、最大公约数）」免费吗？需要注册吗？Is the LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD) free? Do I need an account?
「最小公倍数计算器（多个数、质因数分解、最大公约数）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The LCM Calculator (Least Common Multiple of Several Numbers, Prime Factorisation, GCD) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.