H.C.F and L.C.M of Decimal Fractions

The highest common factor is commonly known as H.C.F and the lowest common multiple is termed as L.C.M. The H.C.F and L.C.M. of decimal fractions can be found out by various techniques. There are different formulas to find the H.C.F and L.C.M of a decimal fraction. The H.C.F and the L.C.M of decimal fractions can be obtained by understanding what actually H.C.F and L.C.M is. The numerators and the denominators are required in this process. The numerators and the denominators are used in order to find the H.C.F and L.C.M of decimal fractions.

Difference between fraction and decimal fraction

It’s easy to understand the concept with examples. Suppose the decimal form of the numbers 0.6 and 0.9 is given. 0.6 is the decimal part, which can further be written into 6/10 and simply converted into ⅗, which becomes the fraction. It cannot be further simplified. The decimal 0.9 can be written into fraction 9/10, which cannot be made into a simpler form; the HCF and LCM of decimal fractions can be determined by using simple formulas.

What are H.C.F. and L.C.M of decimal fractions?

The H.C.F of decimal fractions is basically the division of H.C.F of numerators to that of L.C.M of denominators. The L.C.M of decimal fractions is found by the division of L.C.M of all the numerators to that of H.C.F of denominators.

How to find H.C.F. and L.C.M of decimal fractions

The H.C.F. and L.C.M of decimal fractions can be calculated by the same formula of finding H.C.F and L.C.M of fractions. The decimal fractions are converted to fractions at first. In order to find the H.CF and L.C.M. of decimal fractions, it must be kept in mind that the fractions must be in their lowest terms. The fractions are required to be converted in their lowest forms if they are in their highest forms. The H.C.F of the decimal fractions, which is required, is considered as the highest fraction, which divides exactly each of the fractions. The L.C.M of the decimal fraction, which is required when two or more fractions are given, is also exactly divisible by each of them. In the case of H.C.F and L.C.M of the decimal fractions, the H.C.F of the numbers is in a fraction always whereas the L.C.M is not true in such a case.

How to find H.C.F of Decimal fractions?

When the question is “how to find H.C.F of decimal fractions”, the formula used is:  H.C.F of the numerators is divided with L.C.M of all denominators. 

Suppose the example of 36/51 and 60/17 are taken in order to find the H.C.F of a decimal fraction. The fraction needs to be converted into the simplest form in order to find the H.C.F of a decimal fraction. Therefore, 36/51 can be converted into the simplest form of 12/17. Then according to the given formula, the required H.C.F can be calculated by finding the H.C.F of the numerators 12 and 60. The H.C.F of 12 and 60 is 12. Then the L.C.M. needs to be determined for 12 and 17, which is definitely 17. Therefore, the answer to the given example is 12/17.

How to find L.C.M of Decimal fractions?

When the question is “how to find L.C.M of decimal fractions”, the formula used is: L.C.M of numerators divided by H.C.F. of denominators.

Suppose three fractions are taken such as 126/75, 72/250,162/165 in order to find the L.C.M of a decimal fraction. First, to find the L.C.M of decimal fractions converting the given fractions into simpler fractions is required. The fraction 126/75 can be converted into 42/25. The fraction 72/250 can be converted into 36/125. The fraction 162/165 can be converted into 54/55. As soon as the conversion process is complete, the simpler fractions need to be put into the formula.

Another example where the direct decimal is provided such as 0.6, 0.12, and 9.6 is given. To find the L.C.M of decimal fractions, the numbers can be written as 6/10, 12/100, and 96/10. Therefore the L.C.M of the numerators 6, 12, 96 is 96 and the H.C.F. of 10, 100, and 10 is 10. Therefore, the answer is 96/10, which is equal to 9.6.

Conclusion

From the above discussion, it can be concluded that the H.C.F and L.C.M of decimal fractions can be found out by using simple formulas. The numerators and the denominators of the given decimal fractions are used in the process. The HCF and the LCM of the decimal fractions can also be found out using the simpler techniques. In the H.C.F and L.C.M. of the decimal fractions, the prime factorization methods and the division methods are easy to solve by which decimal fractions can be easily determined.