如何找到4个数字的LCM？

在寻找最小公倍数之前，我们必须知道数字系统。在这个数系中，我们可以学习自然数、整数、整数和有理数。如果我们对数字系统有一个想法，我们就可以识别它是什么类型的数字？这样我们就可以轻松地找到 LCM，并且我们将了解我们必须找到 LCM 的数字以及找到因子或除数的最简单方法是什么。

例如，从 1 到无穷大的数字是自然数，包括零的数字是整数，数字以负数和正数开头，零也是整数，a/b 形式的数字是有理数。

什么是数字系统？

数字系统是一种以书面形式表示或表达数字的方式，例如在数学符号中使用数字。这个数字就像计算我们现实世界活动中的物体或数字一样。

示例：自然数集表示为 {1, 2, ...} 是我们称为自然数的数字。与自然数一样，我们有整数、整数、复数和有理数。

• 自然数：自然数是计数的数字，如 1、2、3、4 等，它们只是正数，0 不是自然数。
• 整数：整数在自然数中包含零。一组 0、1、2、3 等是正数，这些整数中不包含负数。所有自然数都可以是整数，但所有整数不必是自然数。
• 整数：整数有负数和整数。一组 {..., -2, -1, 0, 1, 2, 3, ...} 是整数。所有整数都是整数，但所有整数都不是整数。
• 有理数：有理数包括所有整数、分数和小数。有理数可以表示为 a/b 形式。 3 可以表示为 3/1。所以它是一个有理数，3.33也可以表示为3.33/1。

什么是液晶模组？如何找到它？

LCM is abbreviated as a Least Common Multiple. The Least Common Multiple of four numbers or any number of numbers is the smallest common number which is non zero and also it should be a multiple of numbers for which we are finding the Least Common Multiple. Multiple is when we are dividing a given number with a number and leaving no remainder is called multiple of the given number.

例如，假设我们有一个数字 16，它可以被 1、2、4、8 整除，而 16 本身就是给定数字 16 的各种倍数。

• 16 = 1×16 或（16/1=16 和 16/16 = 1 所以除法时没有余数称为倍数。1,16 是倍数）
• 16 = 2×8 或（16/2=8 和 16/8 = 2 其中 2 和 8 是 16 的倍数）
• 16 = 4×4 或（16/4 = 4，其中 4 是商和倍数，但除法时没有余数）

确定 LCM 的方法

有不同的方法可以找到两个或多个数字的 LCM：

1. LCM 使用素因子分解法。
2. LCM 使用重复除法或长除法。
3. LCM 使用数字的倍数。

使用素数分解法的 LCM

Before going into this we have to know factorization and that to prime factorization. Prime numbers are the numbers that have only two factors are 1 and themselves.

For Example, 3 is a prime number because 3 can have factors 1 and 3. 

• 1 is a factor of 3 because 1×3 is 3
• 3 is a factor of 3 because 3×1 is 3

素数分解是一种使数字成为素数乘积的方法。

使用素数分解的 10、12、14、16 的 LCM 表示为，

使用素数分解的 LCM

• 10 = 2 × 5
• 12 = 2 × 2 × 3
• 14 = 2 × 7
• 16 = 2 × 2 × 2 × 2

在每个数的上述因数中，所有数中只有 2 是共同的，所以 2×2×2×2×3×5×7 = 1680 是 10、12、14、16 的 LCM。

LCM 使用重复除法或长除法。

In this method, numbers are divided with the common divisors until no further possible division occurs. Divisors are the numbers in which we have to divide a number with another number that another number is called the divisor.

For Example, Suppose the number 12 is divided by either 1, 2, 3, 4, 6, or 12.

• 12 = 2×6 because we can able to written 12 as 2×6 so 2 and 6 are divisors of 12.
• 12 = 4×3 because we can able to write 12 as 4×3 so 4 and 3 are divisors of 12.
• 12 = 12×1 because of this we can able to write as 12×1 so, 1, 12 are divisors of 12.

LCM of 10,12,14,16 using Repeated division is expressed below.

LCM using repeated division

So from here if we multiply divisor and remainder we get LCM of 10, 12, 14, 16.

LCM = 2×2×2×5×3×7×2 = 1680

LCM 使用数字的倍数

Finding LCM using multiples is the selecting first most common multiple among the group of multiples of numbers. When we are dividing a given number with a number and leaving no remainder is called a multiple of the given number.

For Example, LCM of 2,4,6,8 is the first common multiple among the multiples of 2, 4, 6, 8.

LCM using Multiples 

In the above figure, it is the table form of multiples of 2, 4, 6, 8. In the above table, 24 is the LCM of 2, 4, 6, 8 because it is the first common multiple of all the numbers 2, 4, 6, 8.

液晶模组的特性

• 至少两个数字的 LCM 不能不完全或小于其中任何一个。例如，3,4,5,6 的 LCM 是 60，它不小于任何给定数字 (3,4,5,6)。
• 一个数的因数及其 LCM 大于该数本身。例如，4,8 的 LCM 为 8。

示例问题

问题一：10、20、30、40这一系列数字的LCM是多少？

回答：

This question is solved by using the repeated division method as,

10, 20, 30, 40 can be written as follows:

• 10 = 2×5 where 2 and 5 are prime numbers.
• 20 = 2×10=2×2×5, so here also 10 again written as 2×5 so all are prime numbers. 

Similarly, 

• 30 can be written as 30=3×10 and again 10 can be written as 2×5 so 2, 3, and 5 are prime numbers.
• 40 = 2×20=2×2×10=2×2×2×5.

LCM in a detailed way for this problem is shown as:

LCM(10,20,30,40)=120

The above method of finding LCM is Repeated division discussed in the types for finding LCM.

Therefore, LCM (10, 20, 30, 40) = 120 (Since, 2×2×5×2×3×1×1 is 120).

问题2：数字2、3、5、7系列的LCM是多少？

回答：

Here 2, 3, 5, and 7 all are prime numbers so LCM is simply a product of all the given numbers that is 2×3×5×7 is the LCM.

By using repeated division 2 can be written as 2×1, similarly 3=3×1,5=5×1,7=7×1 like that.

So. LCM of 2, 3, 5, 7 is 2×3×5×7=210

Detailed LCM of this problem is given as.

 

The above method of finding LCM is Repeated division discussed in the types for finding LCM.

Therefore LCM (2, 3, 5, 7) = 210 (Since 2×5×7×3×1 is 210).

问题3：数字1、2、3、4系列的LCM是多少？

回答：

Let’s try the multiples method for this question. For this, we have to write multiples of each and every number means we have to write a table of 1, 2, 3, 4 until the first most common multiple occurs.

• 1 multiples are 1×1=1, 1×2=2, 1×3=3, and so on.
• 2 multiples are 2×1=2, 2×2=4, 2×3=6, 2×4=8, and so on.
• 3 multiples are 3×1=3, 3×2=6, 3×3=9, 3×4=12, and so on.
• 4 multiples are 4×1=4, 4×2=8, 4×3=12, and so on.

Detailed LCM of this problem is given as,

We have to write multiples in that table until the most common factor in all the numbers occurs.

LCM (1,2,3,4) =12

The above method of finding LCM is using multiples discussed in the types for finding LCM.

Therefore, LCM (1, 2, 3, 4)=12 (because the least common multiple among all multiples is 12).

问题4：99、66、33、11这一系列数字的LCM是多少？

回答：

Prime factorization contains a prime number we have to write for a series of numbers.

• 99 can be written as 11×9 and again 9 can be written as 3×3 so finally 99=11×3×3 where 11,3,3 are prime numbers.
• 88 can be written as 11×6 and again 6 can be written as 2×3 so finally, 66 =11×2×3 where 11,2,3 are prime numbers.
• 33 can be finally written as 11×3 where 11,3 are prime numbers.
• 11 itself can be written as 11×1 where 11 is a prime number.

Detailed LCM of this problem is given as,

LCM (11,33,66,99) =198

The above method of finding LCM is the prime factorization discussed in the types for finding LCM.

Therefore, LCM(99, 66, 33,11) = 198 (because 11×3×2×3 is 198).

问题5：0、25、16、36这一系列数字的LCM是多少？

解决方案：

Prime factorization contains a prime number we have to write for a series of numbers.

• 4 can be written as 2×2 where 2 is a prime number.
• 6 can be written as 2×3 where 2,3 are prime numbers.
• 25 can be finally written as 5×5 where 5 is a prime number.
• 0 itself can be written as 0×1 

Detailed LCM of this problem is given in the below image.

LCM(0,4,6,25)=300

The above method of finding LCM is the prime factorization discussed in the types for finding LCM.

Therefore LCM(4, 6, 25, 0)=300 (because 2×2×5×5×3 is 300).