LCM Of 32 And 40

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 32 and 40, The LCM is 160. 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 32: 32, 64, 96, 128, 160, 192, 224, 256, 288 and 320.

Multiples Of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400.

The second step is to find the smallest common multiples in both the numbers. In this case, that number is 160 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:

32= 2×2×2×2×2

40= 2×2×2×5

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

So after the multiplication, we will be getting the LCM as 160.

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 16 and 20.

Then we will divide 20 and 16 by 2. This will give us 10 and 8. We will divide this until the last row is just 1. 

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: (2×2×2×2×2×5).

These numbers multiplied give 160. On this basis, therefore, the LCM of the 32 and 40 becomes 160.
 

Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
 

• LCM (The Least Common Multiple): The smallest number that can be evenly divided by two or more numbers.

• Prime Factorization: Breaking a number down into its basic building blocks, called prime numbers, that multiply together to get the original number.

• Prime Number: A number greater than 1 that can only be divided evenly by 1 and itself. Examples include 2, 3, 5, 7, and 11.

• Factors: Numbers that you can multiply together to get another number. For example, 2 and 3 are factors of 6 because 2 × 3 = 6.