least common multiple

简明释义

最小公倍数

英英释义

例句

1.In solving problems involving fractions, knowing the least common multiple (最小公倍数) helps to simplify the addition or subtraction of the fractions.

在解决涉及分数的问题时，知道最小公倍数有助于简化分数的加法或减法。

2.The teacher asked the students to calculate the least common multiple of 6 and 8 for their homework.

老师让学生计算6和8的最小公倍数作为家庭作业。

3.The least common multiple of 3, 4, and 5 is necessary to synchronize the schedules of three different classes.

3、4和5的最小公倍数对于同步三个不同班级的时间表是必要的。

4.When planning events that occur at different intervals, finding the least common multiple (最小公倍数) can help determine when they will coincide.

当计划不同时间间隔发生的事件时，找到最小公倍数可以帮助确定它们何时重合。

5.To find the least common multiple of 4 and 5, we can list the multiples: 4, 8, 12, 16, 20 and 5, 10, 15, 20. The least common multiple (最小公倍数) is 20.

要找4和5的最小公倍数，我们可以列出倍数：4, 8, 12, 16, 20 和 5, 10, 15, 20。最小公倍数是20。

作文

Understanding mathematical concepts is essential for students, as it lays the foundation for more advanced topics in mathematics and other sciences. One such concept that often confuses learners is the least common multiple (LCM). The least common multiple of two or more integers is the smallest positive integer that is divisible by each of the numbers. This definition may sound complex at first, but with some practice, it becomes easier to grasp. To illustrate the concept of the least common multiple, let us consider the numbers 4 and 6. To find the least common multiple, we can list the multiples of each number:- Multiples of 4: 4, 8, 12, 16, 20, 24...- Multiples of 6: 6, 12, 18, 24, 30...By examining these lists, we see that the smallest common multiple is 12. Therefore, the least common multiple of 4 and 6 is 12. This method of listing multiples is straightforward but can be time-consuming, especially with larger numbers.Another efficient way to find the least common multiple is by using the prime factorization method. Each integer can be expressed as a product of prime factors. For example, the prime factorization of 4 is 2², and for 6, it is 2¹ × 3¹. To find the least common multiple, we take the highest power of each prime that appears in the factorizations:- From 4 (2²) we take 2².- From 6 (2¹ × 3¹) we take 3¹.Thus, the least common multiple is calculated as follows:2² × 3¹ = 4 × 3 = 12. This method is particularly useful when dealing with larger numbers or more than two integers.The least common multiple is not only a fundamental concept in mathematics but also has practical applications in real life. For instance, when scheduling events that repeat at different intervals, knowing the least common multiple can help determine when the events will coincide. If one event occurs every 4 days and another every 6 days, they will both occur on the same day every 12 days.Moreover, understanding the least common multiple is crucial for solving problems involving fractions. When adding or subtracting fractions, we need a common denominator, which is often the least common multiple of the denominators involved. For example, if we want to add 1/4 and 1/6, we first find the least common multiple of 4 and 6, which is 12. We then convert the fractions: 1/4 becomes 3/12, and 1/6 becomes 2/12. Now we can easily add them together: 3/12 + 2/12 = 5/12.In conclusion, the least common multiple is a vital concept that enhances our understanding of mathematics and its applications. By mastering this concept, students can solve various mathematical problems more efficiently and apply their knowledge to real-world situations. Whether through listing multiples or using prime factorization, finding the least common multiple becomes an invaluable skill that will benefit learners throughout their academic journey and beyond.

理解数学概念对学生来说至关重要，因为它为更高级的数学和其他科学主题奠定了基础。一个常常令学习者困惑的概念是最小公倍数（LCM）。两个或多个整数的最小公倍数是可以被每个数字整除的最小正整数。这个定义乍一听可能很复杂，但经过一些练习，它变得更容易掌握。为了说明最小公倍数的概念，让我们考虑数字4和6。要找到最小公倍数，我们可以列出每个数字的倍数：- 4的倍数：4，8，12，16，20，24……- 6的倍数：6，12，18，24，30……通过检查这些列表，我们看到最小的共同倍数是12。因此，4和6的最小公倍数是12。这种列出倍数的方法简单明了，但对于较大的数字来说可能会耗时。另一种有效找到最小公倍数的方法是使用质因数分解法。每个整数都可以表示为质因数的乘积。例如，4的质因数分解是2²，而6的质因数分解是2¹ × 3¹。为了找到最小公倍数，我们取出每个质数在分解中出现的最高次幂：- 从4（2²）我们取2²。- 从6（2¹ × 3¹）我们取3¹。因此，最小公倍数的计算如下：2² × 3¹ = 4 × 3 = 12。这种方法在处理较大数字或多个整数时特别有用。最小公倍数不仅是数学中的基本概念，而且在现实生活中也有实际应用。例如，在安排不同间隔重复的事件时，知道最小公倍数可以帮助确定事件何时重合。如果一个事件每4天发生一次，另一个事件每6天发生一次，它们将在每12天的同一天发生。此外，理解最小公倍数对于解决涉及分数的问题至关重要。当我们加减分数时，我们需要一个公共分母，这通常是涉及的分母的最小公倍数。例如，如果我们想加1/4和1/6，我们首先找到4和6的最小公倍数，即12。然后我们将分数转换：1/4变为3/12，1/6变为2/12。现在我们可以轻松地将它们相加：3/12 + 2/12 = 5/12。总之，最小公倍数是一个重要的概念，它增强了我们对数学及其应用的理解。通过掌握这一概念，学生可以更有效地解决各种数学问题，并将他们的知识应用于现实世界的情境中。无论是通过列出倍数还是使用质因数分解，找到最小公倍数都成为一种宝贵的技能，将使学习者在他们的学术旅程及以后的生活中受益。