LCM Of 3,9 and 15

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 3,9 and 15, The LCM is 45. 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.

Step 1: list all the multiples of the given numbers.

Multiples Of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57 and 60.

Multiples Of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81 and 90.

Multiples Of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135 and 150.

Step 2: find the smallest common multiples in both the numbers. In this case, that number is 45 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.

Step 1: break down the given numbers into its primal form. The primal form of the number is:

3= 3

9= 3×3

15= 3×5

Step 2: As you can see, 3 appears as a prime factor in all three numbers. So instead of considering 3 4 times, we will only consider it two times. So the final equation will look like (3×3×5).

So after the multiplication, we will be getting the LCM as 45.

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 3. In that case, we divide the numbers by 3. It will reduce the values of the numbers to 1, 3 and 5.

As 3 and 5 are prime numbers, we will divide those numbers by themselves and get the last to be only 1’s. 

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:3,3 and 5. 

These numbers multiplied give 45. On this basis, therefore, the LCM of the 3,9 and 15 becomes 45.
 

• LCM (The Least Common Multiple): The smallest number that can be evenly divided by two or more numbers without leaving a remainder.

• Multiple: A number that can be obtained by multiplying a given number by an integer. For example, multiples of 3 include 3, 6, 9, 12, etc.

• Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, etc.

• Division Method: A technique to find the LCM by dividing the given numbers by their common prime factors until only 1s remain.