Last updated on May 26th, 2025
The Least Common Multiple (LCM) is the smallest number that when we divide by two or more numbers at a time, all three or more numbers divide into it. LCM also helps in math problems and everyday things like event planning or buying supplies. We will find the LCM of 6, 12 and 15 together and what that really means.
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, 12 and 15, 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:
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 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, and 120.
Multiple Of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150.
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
12= 2×2×3
15= 5×3
As you can see, 2 appears as a prime factor in both numbers. So instead of considering 2 five times, we will only consider it four times. So the final equation will look like (2×2×3×5).
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 3. In that case, we divide the numbers by 3. It will reduce the values of the numbers to 2, 4 and 5.
5 is a prime number, it can be divided by only 5. That means after dividing, there will be only 2 and 4 left. This can be divided by 2 which will bring 4 down to 2 and 2 will be reduced to 1. As 2 is a prime number, it can only be divided by 2. After this step, there will only be 1’s left in the last row.
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: 2,2,3 and 5.
These numbers multiplied give 60. On this basis, therefore, the LCM of the 6, 12 And 15 becomes 60.
Let us look at some of the common mistakes that can happen while solving a given assignment regarding LCM.
If a train arrives every 6 minutes, 12 minutes, and 15 minutes, when will they arrive together?
The trains will arrive together every 60 minutes.
To find when the trains meet, we look for the smallest number that 6, 12, and 15 can all divide into, which is 60.
Sam’s friends come every 6, 12, and 15 days. When will they all come together again?
They will meet every 60 days.
To find when they all meet, find the least common multiple (LCM) of 6, 12, and 15. The LCM is 60, so they meet in 60 days.
Lily cycles every 6 days, Tim every 12, and Max every 15. When will they cycle together?
They will cycle together every 60 days.
Lily cycles every 6 days, Tim every 12, and Max every 15. The smallest number they all share is 60, so they cycle together every 60 days.
Three singers sing every 6, 12, and 15 days. When do they sing together?
They will all sing together again in 60 days.
To find when they sing together, we find the smallest number that 6, 12, and 15 divide into. That number is 60.
If three friends walk every 6, 12, and 15 minutes, when do they meet again?
They meet every 60 minutes.
The three friends walk every 6, 12, and 15 minutes. They will all meet together again after 60 minutes because 60 is the smallest time that divides evenly by 6, 12, and 15.