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# How to find L.C.M. of fractions (with explanation)

Module by: Sukanta Ray. E-mail the author

Summary: It contains the method of finding Least common multiple of fractions and its explanation.

How to find L.C.M of fractions.

First of all, how do we find L.C.M. of some given integers?

We are allowed to multiply the given integers separately by natural numbers. And our target is to pick out the minimum common result.

The same process is applicable in case of finding L.C.M. of some fractions.

Let us start with three fractions 1515 size 12{ { {1} over {5} } } {}, 310310 size 12{ { {3} over {"10"} } } {} and 415415 size 12{ { {4} over {"15"} } } {} .

Here, we are allowed to multiply the given fractions separately by natural numbers. And our target is to pick out the minimum common result.

(a) We will first concentrate on the tops (numerators) of these fractions.

Many common results can be generated at the top (such as, 12, 24, 36, 48 and so on) by separately multiplying 1, 3 and 4 with necessary natural numbers, but to keep them lowest, we will take: 'the product' 'which will come first' 'in all the three numerators'.

In other words we have to find the 'multiple' 'lowest' 'common', which in this case is 12.

So we have found the top portion of our answer as 1212 size 12{ { {"12"} over {} } } {}

Therefore, the Rule is = Find L.C.M. of the tops (numerators).

(b) Next come to the bottoms (denominators) of the fractions.

Next, we proceed to get a common result at the bottom by further multiplications. But in this case, we find that multiplication reduce the denominators into smaller numbers by cancelling factors from them.

To make our final result as lowest as possible, we have to keep its bottom as greater as possible. So we should carry on multiplying the fraction upto that point so that, they all will have the greatest possible common factor left at the bottom.

The G.C.F. in this case is 5. So we have found bottom portion of our answer which is 55 size 12{ { {} over {5} } } {}

So here, the Rule is = Find G.C.F. of the bottoms (denominators).

Thus, our final answer becomes 125125 size 12{ { {"12"} over {5} } } {} .

To sum up, L.C.M. of some fractions = L.C.M of the numeratorsG.C.F. of the denominatorsL.C.M of the numeratorsG.C.F. of the denominators size 12{ { {L "." C "." "M of the numerators"} over {G "." C "." F "." " of the denominators"} } } {}

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