LCM Of 6 And 20

The LCM or the least common multiple of 2 numbers is the smallest number that appears as a multiple of both numbers. In case of 6 and 20, The LCM is 60. But how did we get to this answer? There are different ways to obtain a LCM of 2 or more numbers. Let us take a look at those methods.
 

Remember that we previously said there are plenty of ways to calculate the LCM of two numbers or more. Then some of those methods make it extremely easy for us to find the LCM of any two numbers. Those methods are: 

• Listing of Multiples

• Prime Factorization

• Division Method

Finally, now we will learn how each of these methods can help us to calculate LCM of given numbers.
 

This method will help us find the LCM of the numbers by listing the multiples of the given numbers. Let us take a step by step look at this method.

• The first step is to list all the multiples of the given numbers.

Multiples Of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54 and 60.

Multiples Of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180 and 200.

• The second step is to find the smallest common multiples in both the numbers. In this case, that number is 60 as highlighted above.

By this way we will be able to tell the LCM of given numbers.
 

Let us break down the process of prime factorization into steps and make it easy for children to understand.

• The first step is to break down the given numbers into its primal form. The primal form of the number is:

6= 3×2 

20= 2×2×5

• As you can see, 2 appears as a prime factor in both numbers. So instead of considering 2 three times, we will only consider it two times. So the final equation will look like (3×2×2×5).

• So after the multiplication, we will be getting the LCM as 60.

As you can see, using this method can be easier for larger numbers compared to the previous method. 
 

The method to calculate the LCM is really simple. We’ll break these given numbers apart till it comes down to one, by dividing it by the prime factors. The product of the divisors that will come is the LCM of the given numbers.

Let us understand it step by step:

• The first thing is to find the number common in both the numbers. Here it is 2. In that case, we divide both the numbers by 2. It will reduce the values of the numbers to 3 and 10.

• Then we will divide 10 by 2 and 3 is a prime number. The 10 will be reduced to 5. As both 5 and 3 are prime numbers, it can’t be divided by any other number other than themselves. After this step, the last row will be 1’s.

• As the numbers in the last row now are 1, we will take the numbers on the left side and find the product of those numbers. The final equation will look like this: (3×2×2×5).

These numbers multiplied give 60. On this basis, therefore, the LCM of the 6 and 20 becomes 60.
 

• Multiple: A number that is created by multiplying a given number by an integer. For example, the multiples of 6 are 6, 12, 18, and so on.

• Prime Factor: A number that can only be divided by itself and 1. For example, 2, 3, 5, and 7 are prime numbers.

• Prime Factorization: The process of breaking a number down into its prime factors. For example, 20 can be broken down into 2 × 2 × 5.

• Divisibility: The ability of one number to be divided by another without leaving a remainder. For example, 20 is divisible by 5 because 20 ÷ 5 = 4.