LCM Of 8,12 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 8,12 and 20, The LCM is 120. 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 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128 and 136.

Multiples Of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108 and 120. 

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 120 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:

8= 2×2×2

12= 2×2×3

20=2×2×5

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

So after the multiplication, we will be getting the LCM as 120.

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:

Step 1: 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 4, 6 and 10.

Step 2: We will divide the numbers by 2 again, now it will become 2,3 and 50. As these numbers are prime numbers, it can only be divided by the number itself. After that, one 1’s will be in the last line.

Step 3: This is the end of division. However, we will now find the product of the numbers on the left. The numbers on the left side are: 2,2,2,3 and 5. 

These numbers multiplied give 120. On this basis, therefore, the LCM of the 8,12 and 20 becomes 120.
 

• Multiple: A number you get when you multiply a number by a whole number. For example, the multiples of 2 are 2, 4, 6, 8, and so on.

• Divisibility: When one number can be divided by another number without leaving a remainder. For instance, 15 is divisible by 3 because 15÷3=5.

• Prime Factorization: Breaking down a number into its basic building blocks, which are prime numbers. For example, 12 can be broken down into 2×2×3.

• Divisor: A number that divides another number evenly. For example, 4 is a divisor of 12 because 12÷4=3.