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The H.C.F is also known as the Highest Common Factor for any two given numbers and has been the other number that is possibly counted as the highest. This individual number that is seen as highest can divide both the numerals while leaving no remainder. The same is also identified as the G.C.D and/or Greatest Common Divisor.
The L.C.M., on the other hand, is identified as the Least Common Multiple. The same can be elaborated as the numerical value that is considered the lowest and can be divided by the two given numbers. Not only two numbers, but the L.C.M be also calculated on more than two given integers.
Calculating the H.C.F
As explained, the H.C.F of two numbers can be a comparatively higher number that can divide the two given numbers; there are numerous methods to calculate the same. This does not leave any remainder and can be explained while analysing an example. Considering two distinct numbers such as 150 and 230 and the H.C.F of the two can be calculated while utilising the following method.
150 can be presented as 150= 2x5x5x3 and for 230 the related presentation is 230=2x5x23. Thus, it can be seen that the numbers that are common in this scenario are 2 and 5. Thus the H.C.F and G.C.D can be identified by the product of both the distinct numbers and that is 10. The result of the H.C.F can be represented as HCF (150, 230) =10.
Thus using the aforementioned explanation, a similar calculation can be done on 60 and 40 for an instance where 60= 2x2x3x5 and 40= 2x2x2x5. Here, it can be noted that both the numbers 2, 2, 5 are common and multiplying the three numbers can identify the HCF that is 20.
Calculating the L.C.M
In this scenario, it has been explained that the number that is lowest amidst the common multiples of the given two or more numbers in mathematics. Considering the first step in this exact process, plotting the prime factors of the two numericals is required.
For 15, the two prime factors are 3 and 5. In the scenario for L.C.M, the second step suggests that the common prime factors have been required to be included for once. This individual method is also identified as the “Prime Factorization method”. On the other hand, the calculation of the L.C.M can also be performed by “Prime Factorisation”, during which firstly, all the “Prime factors” have been figured out corresponding with the given number. After that, the “prime number” that has been identified has been listed based on the repetition of the prime number. Moreover, at the end of the calculation all the listed “prime factors” have been multiplied together to get the L. C.M. For better clarification, it can be presented that, regarding of L.C.M 24 and 300, the prime fraternisation of the 24 and 300 will be, (2 Χ2 Χ 2 Χ3) and (2 Χ2 Χ3 Χ5 Χ 5) respectively. Furthermore, after identifying all the prime numbers, the prime numbers that are repeated in manner, that means, 2, 2,3 and 5 will be multiplied. Finally multiplying these prime numbers, which means (2x2x3x5), 60 will be obtained, representing the L.C.M. However, numerous other methods are present, such as the division method, ladder method, Greatest common factor methods and many more are present. All of these methods have been used to calculate the Least Common Multiple.
Product of two numbers is equal to HCF and lcm
This can be considered as a relation between the H.C.F and the L.C.M and the product and/or multiplication of both the given numbers can be observed as equal with the multiplied values of extracted H.C.F and the L.C.M on the same numbers. It can be represented as H.C.F x L.C.M= A x B. In this scenario, character A has been representing the first number and the B is required while representing the second number.
Considering the explained example of the H.C.F and the derived L.C.M for 60 and 40, it has been seen that the H.C.F has been 20. The L.C.M has also been calculated and the result has been 120. These two distinct values can be multiplied and the result can be considered as the product. This value can be placed on the Left Hand Side (L.H.S) of the aforementioned equation and the figure is 240.
Considering the R.H.S and/or the Right Hand Side multiplying the numbers that are 60 and 40 can also be seen as representing the value similar to the L.H.S and that is 2400 as well.
Conclusion
It can be concluded as the LCM and the HCF can be figured out while relying on numerous methods. The prime factors in these scenarios are seen as necessary. It has been noted that prime factorisation has been considered to be comparatively easier. Additionally, the product of the two numbers has been proven as being equal to the product of HCF and LCM of both numbers.
