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 8,12 and 20 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 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:
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.
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.
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.
Let us look at some of the common mistakes that can happen while solving a given assignment regarding LCM.
Three kids run laps: There is one that runs every eight minutes, one that runs every twelve minutes, and the last that runs every twenty minutes. When will they all meet?
They will all meet after 120 minutes.
120 is the smallest number that can be divided by 8, 12, and 20. This is called the least common multiple (LCM).
Three school buses leave at different times: one every 8 minutes, one every twelve minutes, and the last every 20 minutes. When do they leave together?
They leave together every 120 minutes.
The buses leave together every 120 minutes because 120 is the smallest number that can be evenly divided by 8, 12, and 20.
If a baker bakes cookies every 8, 12, and 20 minutes, when will they bake together?
The cookies will bake together every 120 minutes, or 2 hours.
The baker bakes cookies every 8, 12, and 20 minutes. The smallest time when they all bake together is 120 minutes.
Three cars start a race: one every 8, another every 12, and the last every 20 minutes. When do they race together?
The cars will race together after 120 minutes.
120 is the smallest number that fits perfectly into 8, 12, and 20 minutes. This means all cars will start at the same time after 120 minutes.
When should they be planted together if a gardener plants flowers 8, 12, and 20 days apart?
They should all be planted together every 120 days.
Since 120 is the smallest number that can be divided evenly by 8, 12, and 20, they all plant together after 120 days.