Least Common Multiple (L.C.M)

In mathematics, it is a very common process to be followed to solve complex calculations. Application of such solutions provides easy ways to bring results. In the number theory, the process of calculating the least common multiple is very much critical to reaching a solution quickly. To calculate the L.C.M, there are three basic steps that need to be followed. At first, it is very much important to make lists of the numbers, then need to find the smallest number as that small number is the result of the L.C.M. Here, the importance of L.C.M in mathematics has been evaluated.

Concept of the L.C.M

The least common multiple or L.C.M is a very important mathematical calculation process for the arithmetic types of math. To understand the concept, first, it is important to understand the definitions of the L.C.M. least common multiple is the smallest positive integer that can be divided by all numbers that are added to calculate the L.C.M. L.C.M of two given numbers can be calculated by dividing the product of two number with the H.C.F of that two-given number. With the use of such a concept, difficult arithmetic problems can be solved in very quick times. More application of the concept can be observed in the higher degree of complex calculations. To calculate the least common multiple, it is very much important to write the two prime numbers. The wrong process of the calculations can show irrelevant types of results. 

Properties of the L.C.M

To understand the properties of the least common multiple, it is very much important to understand the concept of the L.C.M. mainly in the arithmetic types of mathematical problems, application of the L.C.M concept is Hughes. Some of the properties of the concept’s least common multiple are discussed below. 

• The resultant L.C.M is never coming less than the two or more given numbers. 
• L.C.M of the prime numbers is always the product of all the numbers.
• To calculate the L.C.M of the fraction number needs to divide the LCM of the numerator from the HCF of the denominators. 
• When a number is the factor of another number, the L.C.M will always become greater than the number itself. 

The process of the L.C.M is very much useful and effective. In the case of any difficult calculative mathematical problem in the erythematic, the concept of the least common multiple plays a very important role. 

Methods to found L.C.M

With the help of two different kinds of methods L.C.M of the numbers can be calculated. With the help of the primary factorization method and division calculative methods, the value of the least common multiple can be calculated. The process of listing the multiples of the number can be beneficial in order to calculate the L.C.M. 

In the case of the primary factorization method, first of all, the given number is needed to be written in the form of multiple individually. Then the numbers with the higher degrees are taken along with the single remaining number to determine the exact L.C.M values of the given number.

The division method is the most popular method to determine the L.C.M value of a number. In this method, all given number needs to be divided by the prime numbers. L.C.M obtain by multiplying the primary numbers and the remainders. 

Examples of L.C.M

The concept of the L.C.M is not that much difficult to understand. To calculate the least common multiple of some numbers, the multiplication of the two numbers is divided by the GCD or the great common division. 

L.C.M = L.C.M of number/H.C. F of Denominator

L.C.M (A, B) = (A*B)/GCD (A, B)

These are examples to calculate the value of L.C.M from some numbers. Although this process is very much applicable in the mathematical problems related to arithmetic only.

Conclusion

The concept of the least common multiple is very much important in mathematics. With the help of such a concept, many complex problems can be solved and it makes it easy to calculate some specific types of problems. L.C.M can be divisible by both or every number, which is used to calculate the L.C.M. least common multiple is specifically beneficial to solve arithmetic-related problems. In this paper, the importance of L.C.M in mathematics has been evaluated.