LCM is an acronym, and it stands for the Lowest or Least Common Multiple. The least common multiple (LCM) is the lowest common multiple that is divisible by a given set of numbers. The LCM must be a multiple of all the given numbers. Thus, we can also say that the LCM of given numbers is the smallest number that can appear as a multiple and can be divided by those numbers. In this article, we learn about the properties of LCM and what are the different methods that can be used to calculate it.
Properties of LCM
- The LCM of two or more numbers must not be lesser than any of the given numbers.
- If we are given two numbers, and one of them is a prime number, then the LCM of those numbers is either their product or the larger number itself. For example, The LCM of 4 and 5 is 20 (4 * 5 = 20). The LCM of 5 and 15 is 15.
- If we have two consecutive numbers then the LCM is the product of those given numbers. For example, LCM of 2 and 3 is 6 (2 * 3 = 6).
- The product of two given numbers is equal to the product of the LCM and GCF of those two given numbers.
Methods to Calculate LCM
1. Listing Method
In this method, we need to make a list of all the multiples of the given numbers. The next step is to scan these lists and find the common multiples of the numbers. The multiple with the least value out of all the common multiples gives us the LCM of those given numbers. Let us take a look at an example to clear our concepts.
Find the LCM of 12 and 16 by using the listing method.
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 ….
- Multiples of 16: 16, 32, 48, 64, 80, 96, 112 ….
As we can see, the common multiple with the smallest value is 48. Hence LCM of 12 and 16 is 48.
2. Prime Factorization Method
A major problem associated with the listing method is that the multiples of numbers are endless. When it comes to large numbers finding the common multiple with the smallest value can become very difficult. In such a case, it is best to use the prime factorization method. To find the LCM of numbers using the prime factorization method, we first need to write down the given numbers as a product of their prime factors. The next step is to list down all the prime factors ensuring that common factors between the numbers have been only written down once. To get the LCM, we simply multiply these factors. Let us take a look at an example.
Find the LCM of 12 and 16 using the prime factorization method.
- Prime Factors of 12 = 2 × 2 × 3
- Prime Factors of 16 = 2 × 2 × 2 × 2
- LCM of 12 and 16 is given by 2 × 2 × 2 × 2 × 3 = 48
Thus, regardless of the method used, the LCM of the given numbers will always be the same.
The LCM of numbers is used not only to solve complicated problems but also is widely used in daily-life applications. Thus, it is important for kids to develop a clear foundation of this topic. Cuemath is a fantastic online educational platform that focuses on combining studies with fun to provide kids with a holistic learning environment. With Cuemath, your kids will be able to master Mathematics in no time!