The smallest positive integer that is divisible by the given integers is known as the lowest common multiple or LCM. As the division of integers by zero remains undefined hence, the given numbers cannot be equal to 0. The least common multiple of two numbers m and n is denoted by LCM (m, n). The LCM is also called the smallest common multiple. The concept of LCM is required in the case of unlike fractions, where the denominators have to be converted to the same number to perform simple arithmetic operations such as addition, subtraction, or comparison.
There are many different methods available for the purpose of calculating the LCM of two or more numbers; however, in this article, we will discuss the two most common and simplest methods that can be used by kids who go to school.
Methods to Calculate the LCM of numbers
1. Listing Method
The is the most basic method to calculate the LCM of given numbers. We start by making a list of the initial multiples of the given numbers. The next step is to find the list of the common multiples or multiples that are shared by all the given numbers. This list is endless; hence, we stop when we find the lowest value of the common multiples. This value is the LCM for those numbers. The best way to understand this concept is with the help of an example.
Use the listing method to find the LCM of 4 and 16.
- Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32 ….
- Multiples of 16 = 16, 32, 40 ….
- Common Multiples = 16, 32 ….
- As 16 has the smallest value out of the common multiples hence, the LCM of 4 and 16 is 16.
2. Prime Factorization
We know that the list of multiples of any number is endless. To find common multiples between the given numbers can be a huge task. Hence, we switch to the prime factorization method. In this method, we are required to express all the numbers whose LCM needs to be found as a product of their prime factors. We then make a combined list of all the prime factors ensuring that there are no repeated numbers. Such common factors are written down only once. We eventually multiply all the prime factors to give the LCM of the given numbers. Let us use an example to explain this concept in a better manner.
- Prime Factors of 4 = 2 * 2
- Prime Factors of 16 = 2 * 2 * 2 * 2
- Common Prime Factors = 2 * 2 * 2 * 2
- By multiplying all the prime factors we get the LCM of 4 and 16 that is 16.
Thus, we can see that the LCM of numbers will remain unchanged irrespective of the method used. Once kids can get an in-depth knowledge of how to solve LCM of numbers, they can move on to applying this concept to algebra and attempting more complicated questions. By solving practice problems given in worksheets, a child can increase his speed, accuracy, and reasoning skills.
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